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MR3372695 70H06 37N05 70E15 Shamolin, M. V. [Shamolin, Maxim V.] (RS-MOSC-MC) Classification of integrable cases in the dynamics of a four-dimensional rigid b o dy in a nonconservative field in the presence of a tracking force. (English summary)

Translated from Sovrem. Mat. Prilozh. No. 88 (2013). J. Math. Sci. (N. Y.) 204 (2015), no. 6, 808870. A review for this item is in process. c Copyright American Mathematical Society 2015

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MR3372693 34A30 34E05 37J35 70H06 Okunev, Yu. M. (RS-MOSC-MC) ; Shamolin, M. V. [Shamolin, Maxim V.] (RS-MOSC-MC) On the construction of the general solution of a class of complex nonautonomous equations. (English summary)

Translated from Sovrem. Mat. Prilozh. No. 88 (2013). J. Math. Sci. (N. Y.) 204 (2015), no. 6, 787799. A review for this item is in process. c Copyright American Mathematical Society 2015

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MR3372690 37F50 30D05 Aidagulov, R. R. [A idagulov, R. R.] (RS-MOSC-NDM) ; Shamolin, M. V. [Shamolin, Maxim V.] (RS-MOSC-MC) Top ology on p olynumb ers and fractals.

Translated from Sovrem. Mat. Prilozh. No. 88 (2013). J. Math. Sci. (N. Y.) 204 (2015), no. 6, 760771. A review for this item is in process. c Copyright American Mathematical Society 2015

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MR3372689 Aidagulov, R. Shamolin, M. Polynumb ers,

53C60 51P05 83A05

R. [A idagulov, R. R.] (RS-MOSC-NDM) ; V. [Shamolin, Maxim V.] (RS-MOSC-MC) norms, metrics, and p olyingles.

Translated from Sovrem. Mat. Prilozh. No. 88 (2013). J. Math. Sci. (N. Y.) 204 (2015), no. 6, 742759. A review for this item is in process. c Copyright American Mathematical Society 2015

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MR3372688 53C60 53B40 Aidagulov, R. R. [A idagulov, R. R.] (RS-MOSC-NDM) ; Shamolin, M. V. [Shamolin, Maxim V.] (RS-MOSC-MC) Finsler spaces, bingles, p olyingles, and their symmetry groups.

Translated from Sovrem. Mat. Prilozh. No. 88 (2013). J. Math. Sci. (N. Y.) 204 (2015), no. 6, 732741. A review for this item is in process. c Copyright American Mathematical Society 2015

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MR3297539 70E55 Shamolin, Maxim V. (RS-MOSC-MC) Dynamical p endulum-like nonconservative systems. (English summary)

Applied non-linear dynamical systems, 503525, Springer Proc. Math. Stat., 93, Springer, Cham, 2014. This item will not be reviewed individually. {For the entire collection see MR3297501} c Copyright American Mathematical Society 2015

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MR3287541 91B14 Polyakov, N. L. (RS-MOSC-NDM) ; Shamolin, M. V. [Shamolin, Maxim V.] (RS-GUMF) On a generalization of a theorem of Arrow. (Russian) Dokl. Akad. Nauk 456 (2014), no. 2, 143145; translation in Dokl. Math. 89 (2014), no.

3, 290292. A review for this item is in process. c Copyright American Mathematical Society 2015

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MR3219867 70E15 70G65 Shamolin, M. B. [Shamolin, Maxim V.] (RS-MOSC-IMC) Erratum: "A new case of integrability in transcendental functions in the dynamics of solid b o dy interacting with the environment" [Autom. Remote Control 8, 1378 (2013)] [ MR3224103]. Autom. Remote Control 74 (2013), no. 10, 1771.

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MR3207078 (Review) 37L25 70E15 Shamolin, M. V. [Shamolin, Maxim V.] (RS-MOSC-MC) Some questions of qualitative theory in dynamics of systems with the variable dissipation. Translated from Sovrem. Mat. Prilozh. No. 78 (2012). J. Math. Sci. (N. Y.) 189 (2013), no. 2, 314323.

Summary: "In this work, we consider some problems of the qualitative theory of ordinary differential equations; the study of dissipative systems, as well as variable dissipation system considered below, which, in particular, arise in the dynamics of a rigid body interacting with a medium and in the oscillation theory, depends on solutions of these problems. We consider such problems as existence and uniqueness problems for tra jectories having infinitely remote points as limit sets for systems on the plane, elements of qualitative theory of monotone vector fields, and also existence problems for families of long-period and Poisson stable tra jectories. In conclusion, we study the possibility of extending the Poincarґ two-dimensional topographical system and the comparison e

system to the many-dimensional case."
References

1. S. A. Agafonov, D. V. Georgievskii, and M. V. Shamolin, "Certain topical problems of geometry and mechanics," In: Abstracts of Sessions of the Workshop "Topical Problems of Geometry and Mechanics," Contemporary Mathematics. Fundamental Directions [in Russian], 23 (2007), p. 34. 2. D. V. Georgievskii and M. V. Shamolin, "On kinematics of a rigid body with fixed point in Rn ," In: Abstracts of Sessions of the Workshop "Topical Problems of Geometry and Mechanics," Fundam. Prikl. Mat. [in Russian], 7, No. 1 (2001), p. 315. 3. D. V. Georievskii and M. V. Shamolin, "Kinematics and mass geometry of a rigid body with a fixed point in Rn ," Dokl. Ross. Akad. Nauk, 380, No. 1, 4750 (2001). MR1867984 (2003a:70002) 4. D. V. Georgievskii and M. V. Shamolin, "Generalized dynamical Euler equations for a rigid body with fixed point in Rn ," Dokl. Ross. Akad. Nauk, 383, No. 5, 635637 (2002). MR1930111 (2003g:70008) 5. D. V. Georgievskii and M. V. Shamolin, "First integrals of equations of motion of a generalized gyroscope in Rn ," Vestn. MGU, Mat., Mekh., No. 5, 3741 (2003). MR2042218 (2004j:70012) 6. D. V. Georgievskii and M. V. Shamolin, "Valerii Vladimirovich Trofimov," In: Abstracts of Sessions of the Workshop "Topical Problems of Geometry and Mechanics," Contemporary Mathematics. Fundamental Directions [in Russian], 23 (2007), pp. 56. MR2342521 7. D. V. Georgievskii and M. V. Shamolin, "On kinematics of a rigid body with fixed point in Rn ," In: Abstracts of Sessions of the Workshop "Topical Problems of Geometry and Mechanics," Contemporary Mathematics. Fundamental Directions [in Russian], 23 (2007), pp. 2425. 8. D. V. Georgievskii and M. V. Shamolin, "Generalized dynamical Euler equations for a rigid body with fixed point in Rn ," In: Abstracts of Sessions of the Workshop "Topical Problems of Geometry and Mechanics," Contemporary Mathematics. Fundamantal Directions [in Russian], 23 (2007), p. 30. 9. D. V. Georgievskii and M. V. Shamolin, "First integrals of equations of motion of a generalized gyroscope in n-dimensional space," In: Abstracts of Sessions of the Workshop "Topical Problems of Geometry and Mechanics," Contemporary Mathematics. Fundamental Directions [in Russian], 23 (2007), p. 31. 10. D. V. Georgievskii, V. V. Trofimov, and M. V. Shamolin, "Geometry and mechanics: Problems, approaches, and methods," In: Abstracts of Sessions of the Workshop "Topical Problems of Geometry and Mechanics," Fund. Prikl. Mat. [in Russian], 7, No. 1 (2001), p. 301752. 11. D. V. Georgievskii, V. V. Trofimov, and M. V. Shamolin, "Geometry and mechanics: Problems, approaches, and methods," In: Abstracts of Sessions of the Workshop "Topical Problems of Geometry and Mechanics," Contemporary Mathematics. Fundamental Directions [in Russian], 23 (2007), p. 16. 12. M. V. Shamolin, "The problem of four-dimensional rigid body motion in a resisting medium and one integrability case," In: Book of Abstracts, Third Int. Conf. "Differential Equations and Applications," St. Petersburg, Russia, June 1217, 2000 [in Russian]; StPbGTU, St. Petersburg (2000), p. 198. 13. M. V. Shamolin, "Jacobi integrability of the problem of four-dimensional rigid body motion in a resisting medium," In: Abstracts of Reports of the International Confer-

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ence on Differential Equations and Dynamical Systems (Suzdal, 2126.08.2000) [in Russian], Vladimir State University, Vladimir (2000), pp. 196197. M. V. Shamolin, "Comparison of certain integrable cases from two-, three-, and fourdimensional dynamics of a rigid body interacting with a medium," In: Abstracts of Reports of the Vth Crimean International Mathematical School "Lyapunov Function Method and Its Applications" (MFL2000) (Crimea, Alushta, 0513.09.2000) [in Russian], Simferopol (2000), p. 169. M. V. Shamolin, "On a certain Jacobi integrability case in the dynamics of a four-dimensional rigid body interacting with a medium," In: Abstracts of Reports of the International Conference on Differential and Integral Equations (Odessa, 1214.09.2000) [in Russian], AstroPrint, Odessa (2000), pp. 294295. M. V. Shamolin, "Jacobi integrability in the problem of four-dimensional rigid-body motion in a resisting medium," Dokl. Ross. Akad. Nauk, 375, No. 3, 343346 (2000). MR1833828 (2002c:70005) M. V. Shamolin, "Integrability of the problem of four-dimensional rigid-body motion in a resisting medium," In: Abstracts of Sessions of the Workshop "Topical Problems of Geometry and Mechanics," Fundam. Prikl. Mat. [in Russian], 7, No. 1 (2001), p. 309. M. V. Shamolin, "New integrable cases in the dynamics of a four-dimensional rigid body interacting with a medium," In: Dynamical Systems Modeling and Stability Investigation. Scientific Conference (2225.5.2001) [in Russian], Abstracts of Conference Reports, Kiev (2001), p. 344. M. V. Shamolin, "New Jacobi integrable cases in the dynamics of a two-, three-, and four-dimensional rigid body interacting with a medium," In: Abstracts of Reports of the VIIIth Al l-Russian Session in Theoretical and Applied Mechanics (Perm, 2329.08.2001) [in Russian], Ural Department of the Russian Academy of Sciences, Ekaterinburg (2001), pp. 599600. M. V. Shamolin, "New integrable cases in the dynamics of a two-, three-, and four-dimensional rigid body interacting with a medium," In: Abstracts of Reports of the International Conference on Differential Equations and Dynamical Systems (Suzdal, 0106.07.2002) [in Russian], Vladimir State University, Vladimir (2002), pp. 142144. M. V. Shamolin, "On a certain integrable case in dynamics on so(4) в Rn ," In: Abstracts of Reports of the Al l-Russian Conference "Differential Equations and Their Applications" (SamDif2005), Samara, June 27 July 2, 2005 [in Russian], Univers-grup, Samara (2005), pp. 9798. M. V. Shamolin, "On a certain integrable case of dynamics equations on so(4) в Rn ," Usp. Mat. Nauk, 60, No. 6, 233234 (2005). MR2225204 (2007a:70009) M. V. Shamolin, "On a case of complete integrability in the dynamics of a fourdimensional rigid body," In: Abstracts of Reports on Differential Equations and Dynamical Systems, Vladimir, 1015.07.2006 [in Russian], Vladimir State University, Vladimir (2006), pp. 226228. M. V. Shamolin, "Integrability of the problem of four-dimensional rigid-body motion in a resisting medium," In: Abstracts of Sessions of the Workshop Topical Problems of Geometry and Mechanics," Contemporary Mathematics. Fundamental Directions [in Russian], 23 (2007), p. 21. M. V. Shamolin, "New integrable cases in the dynamics of a four-dimensional rigid body interacting with a medium," In: Abstracts of Sessions of the Workshop "Topical Problems of Geometry and Mechanics," Contemporary Mathematics. Fundamental Directions [in Russian], 23 (2007), p. 27. M. V. Shamolin, "On integrability of motion of a four-dimensional rigid body, a

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pendulum, being in over-run medium flow," In: Abstracts of Sessions of the Workshop "Topical Problems of Geometry and Mechanics," Contemporary Mathematics. Fundamental Directions [in Russian], 23 (2007), p. 37. M. V. Shamolin, "A case of complete integrability in the dynamics of a fourdimensional rigid body in a nonconservative force field," In: Abstracts of Reports of the International Congress "Nonlinear Dynamical Analysis-2007," St. Petersburg, June 48, 2007 [in Russian], St. Petersburg State University, St. Petersburg (2007), p. 178. M. V. Shamolin, "Case of complete integrability in the dynamics of a fourdimensional rigid body in a nonconsevative force field," In: Abstracts of Reports of the International Conference "Analysis and Singularities," Devoted to the 70th Anniversary of V. I. Arnold, Moscow, August 2024, 2007 [in Russian], MIAN, Moscow (2007), pp. 110112. M. V. Shamolin, "Methods of analysis of dynamics of a 2D- 3D- or 4D-rigid body with a medium," In: Abstr. Short Commun. Post. Sess. of ICM2002, Beijing, 2002, August 2028, Higher Education Press, Beijing, China (2002), p. 268. M. V. Shamolin, "4D rigid body and some cases of integrability," In: Abstracts of ICIAM07, Zurich, Switzerland, June 1620, 2007, ETH Zurich (2007), p. 311. M. V. Shamolin, "Cases of integrability in 2D-, 3D- and 4D-rigid body," In: Abstr. of Brief Commun. and Post. of Int. Conf. "Dynamical Methods and Mathematical Modeling," Val ladolid, Spane (Sept. 1822, 2007), ETSII, Valladolid (2007), p. 31.
Note: This list reflects references listed in the original paper as accurately as possible with no attempt to correct errors.

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MR3207076 (Review) 35R35 35K25 Selivanova, N. Yu. (RS-AOS-TI) ; Shamolin, M. V. [Shamolin, Maxim V.] (RS-MOSC-MC) Quasi-stationary Stefan problem with values on the front dep ending on its geometry. (English summary) Translated from Sovrem. Mat. Prilozh. No. 78 (2012). J. Math. Sci. (N. Y.) 189 (2013), no. 2, 301310.

Summary: "The problem presented below is a singular-limit problem of the extension of the Cahn-Hilliard model obtained via introducing the asymmetry of the surface tension tensor under one of the truncations (approximations) of the inner energy."
References

1. G. I. Barenblat, V. M. Entov, and V. M. Rizhik, Behavior of Fluids and Gases in Porous Media [in Russian], Nedra, Moscow (1984). 2. V. T. Borisov, "On mechanism of normal crystal growth," Dokl. Akad. Nauk SSSR, 151, 13111314 (1963). 3. J. W. Cahn and J. E. Hilliard, "Free energy of a non-uniform system, Part I: Interfacial free energy," J. Chemical Physics, 28, No. 1, 258267 (1958).

4. W. Dreyer and W. H. Muller, "A study of the coarsening in tin/lead solders," Int. J. Solids Structures, 37, 38413871 (2000). 5. M. Fabbri and V. R. Voller, "The phase-field method in the sharp-interface limit: A comparison between model potentials," J. Comput. Phys., 130, 256265 (1997). 6. G. Fix, "Phase field models for free boundary problems," In: Free Boundary Problems: Theory and Application, Pittman, London (1983), pp. 580589. 7. P. C. Hohenberg and B. I. Halperin, "Theory of dynamic critical phenomena," Rev. Mod. Phys., 49, 435479 (1977). 8. V. I. Mazhukin, A. A. Samarskii, O. Kastel'yanos, and A. V. Shapranov, "Dynamical adaptation method for nonstandard problems with large gradients," Mat. Model., 5, 3356 (1993). 9. A. M. Meiermanov, Stefan Problem [in Russian], Nauka, Novosibirsk (1986). 10. O. Penrose and P. Fife, "On the relation between the standard phase-field model and a "thermodynamically consistent" phase-field model," Physica D, 69, 107113 (1993). MR1245658 11. E. V. Radkevich and M. Zakharchenko, "Asymptotic solyution of extended Cahn Hilliard model," In: Contemporary Mathematics and Its Applications [in Russian], 2, Institute of Cybernetics, Tbilisi (2003). MR1955051 (2006c:35307) 12. V. A. Solonnikov and E. V. Frolova, "On fulfillment of quasi-stationary approximation for Stefan problem," Zap. Nauchn. Sem. LOMI, 348, 209253 (2007). 13. A. R. Umantsev, "Plane front motion under crystallization," Kristal lografiya, 30, 153160 (1985).
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MR3207075 (Review) 35R35 35J05 Selivanova, N. Yu. (RS-AOS-TI) ; Shamolin, M. V. [Shamolin, Maxim V.] (RS-MOSC-MC) Lo cal solvability of the capillary problem. (English summary) Translated from Sovrem. Mat. Prilozh. No. 78 (2012). J. Math. Sci. (N. Y.) 189 (2013), no. 2, 294300.

Summary: "This paper studies conditions for local (in time) solvability of a qualitatively new singular-limit problem, the free (unknown) boundary problem appearing recently. In fact, there are not so many different free boundary problems, which corresponds to not so large a variety of principally different phase transitions of the first and second kinds. Therefore, the appearance of principally new problems elicits interest. This paper studies structural features of a certain problem on the basis of a certain method developed previously, precisely, the localization method [A. A. Arkhipova, in Linear and nonlinear partial differential equations. Spectral asymptotic behavior, 149 157, Probl. Mat. Anal., 9, Leningrad. Univ., Leningrad, 1984; MR0772048 (86f:35032); S. S. Petrova and M. G. Bulycheva, Istor.-Mat. Issled. No. 31 (1989), 3851; MR0993177 (90e:01022); E. V. Radkevich and M. V. Zakharchenko, Sovrem. Mat. Prilozh. No. 2,

Differ. Uravn. Chast. Proizvod. (2003), 121138; MR1955051 (2006c:35307)]."
References

1. A. A. Arkhipova, "On limit smoothness of solution of a non-stationary problem with one or two obstacles," Probl. Mat. Anal., No. 9, 149156 (1983). 2. I. Athanasopoulous, "Regularity of the solution of an evolution problem with inequalities on the boundary," Commun. Part. Differ. Equ., 7, 14531465 (1982). MR0679950 (84m:35052) 3. M. G. Bulycheva and S. S. Petrova, "From Newton's polygon history," In: Historical Mathematical Studies [in Russian], Issue XXXI, Nauka, Moscow (1989). MR0993177 (90e:01022) 4. I. I. Danilyuk, "On the Stefan problem," Usp. Mat. Nauk, 40, No. 5(245), 133185 (1985). MR0810813 (87d:35003) 5. A. Friedman, Variational Principles and Free Boundary Problems [Russian translation], Nauka, Moscow (1990). MR1140407 (92k:35005) 6. S. Lukkhaus and P. I. Plotnikov, "Entropy solutions of BuckleyLeverett," Sib. Mat. Zh., 41, No. 2. 400420 (2000). MR1762192 (2002e:76019) 7. A. M. Meiermanov, Stefan Problem [in Russian], Nauka, Novosibirsk (1986). 8. E. V. Radkevich and A. K. Melikulov, Free Boundary Problems [in Russian], FAN, Tashkent (1988). 9. E. V. Radkevich and M. Zakharchenko, "Asymptotic solution of extended Cahn Hilliard model," In: Contemporary Mathematics and Its Applications [in Russian], 2, Institute of Cybernetics, Tbilisi (2003), pp. 121138. MR1955051 (2006c:35307) 10. L. R. Volevich and S. G. Gindikin, Newton's Polygon Method in Theory of Partial Differential Equations [in Russian], Editorial URSS, Moscow (1989).
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MR3207074 (Review) 35R35 35K25 Selivanova, N. Yu. (RS-AOS-TI) ; Shamolin, M. V. [Shamolin, Maxim V.] (RS-MOSC-MC) Studying the interphase zone in a certain singular-limit problem. (English summary) Translated from Sovrem. Mat. Prilozh. No. 78 (2012). J. Math. Sci. (N. Y.) 189 (2013), no. 2, 284293.

Summary: "An important role in studying the classical Cahn-Hilliard problem [J. W. Cahn and J. E. Hilliard, J. Chem. Phys. 28 (1958), no. 2, 258267, doi:10.1063/1.1744102] is played by its singular-limit problem, the so-called MelinSikerk free boundary problem, which, at present allows one to only numerically describe the instability of the crystallization process. The purpose of this work is to prepare the material for deducing the singular-limit problem for the essentially asymmetric model [W. Dreyer and W. H. Muller, Int. J. Solids Struct. 37 (2000), Ё

no. 28, 38413871, doi:10.1016/S0020-7683(99)00146-8; E. V. Radkevich and M. V. Zakharchenko, Sovrem. Mat. Prilozh. No. 2, Differ. Uravn. Chast. Proizvod. (2003), 121138; MR1955051 (2006c:35307)]."
References

1. R. Akhmerov, "On structure of a set of solutions of Dirichlet boundary-value problem for stationary one-dimensional forward-backward parabolic equation," Nonlinear Anal. Theory Meth. Appl., 11, No. 11, 13031316 (1987). MR0915527 (89a:35105) 2. N. Alikakos, P. Bates, and G. Fusco "Slow motion for CahnHilliard equation," SIAM J. Appl. Math., 90, 81135 (1991). MR1094451 (92a:35152) 3. G. I. Barenblat, V. M. Entov, and V. M. Rizhik, Behavior of Fluids and Gases in Porous Media [in Russian], Nedra, Moscow (1984). 4. P. Bates and P. Fife "The dynamics of nucleation for CahnHilliard equation," SIAM J. Appl. Math. 53, 9901008 (1993). MR1232163 (94g:82034) 5. J. W. Cahn and J. E. Hilliard, "Free energy of a nonuniform system, Part I: Interfacial free energy," J. Chemical Physics, 28, No. 1, 258267 (1958). 6. V. G. Danilov, G. A. Omel'yanov, and E. V. Radkevich, "Hogoniot-type conditions and weak solutions to the phase field system," Eur. J. Appl. Math., 10, 5577 (1999). MR1685820 (2000b:80005) 7. V. G. Danilov, G. A. Omel'yanov, and E. V. Radkevich, "Asymptotic solution of the conserved phase field system in the fast relaxation case," Eur. J. Appl. Math., 9, 121 (1998). MR1617005 (99c:80005) 8. W. Dreyer and W. H. Muller, "A study of the coarsening in tin/lead solders," Int. J. Solids Structures, 37, 38413871 (2000). 9. Ch. Elliott, "The Stefan problem with non-monotone constitutive relations," IMA J. Appl. Math., 35, 257264 (1985). MR0839202 (87j:35183) 10. Ch. Elliot and S. Zheng, "On the ChanHilliard equation," Arch. Ration. Mech. Anal., 96, No. 4, 339357 (1986). MR0855754 (87k:80007) 11. A. Fridman, Variational Prnciples and Free Boundary Problem, Wiley, New YorkChichester, Brisbane, Toronto, Singapore (1982). 12. C. Grant, "Spinodal decomposition for the CahnHilliard equation," Commu. Part. Differ. Equat., 18, Nos. 34, 453490 (1985). MR1214868 (94b:35147) 13. D. Hilhorst, R. Kersner, E. Logak, and M. Mimura, "On some asymptotic limits of the Fisher equation with degenerate diffusion" (in press). 14. K. Hollig, "Existence of infinity many solutions for a forward-backward parabolic equation," Trans. Am. Math. Soc., 278, No. 1, 299316 (1983). MR0697076 (84m:35062) 15. D. Kinderlehrer and P. Pedregal, "Weak convergence of integrands and the Young measure representation," SIAM J. Math. Anal., 23, 119 (1992). MR1145159 (92m:49076) 16. B. Nicolaenko, B. Scheurer, and R. Temam, "Some global properties of a class of pattern formation equations," Commun. Part. Differ. Equ., 14, No. 2, 245297 (1989). MR0976973 (90e:35138) 17. L. Nirenberg, Topics on Nonlinear Functional Analysis, Courant Inst. Math. Sciences, New York (1974). MR0488102 (58 #7672) 18. P. Plotnikov, "Singular limits of solutions to CahnHilliard equation" (in press). 19. E. V. Radkevich, "Existence conditions of a classical solution of modified Stefan problem (GibbsThomson law)," Mat. Sb., 183, No. 2, 77101 (1982). 20. E. V. Radkevich, "On asymptotic solution of phase field system," Differ. Uravn.,

29, No. 3, 487500 (1993). MR1236336 (94f:35156) 21. E. V. Radkevich and M. Zakharchenko, "Asymptotic solution of extended Cahn Hilliard model," In: Contemporary Mathematics and Its Applications [in Russian], 2, Institute of Cybernetics, Tbilisi (2003), pp. 121138. MR1955051 (2006c:35307) 22. P. G. Saffman and G. I. Taylor, "The penetration of a fluid into porous medium or Hele-Shaw cell containing a more viscous liquid," Proc. Roy. Soc. London, A. 245, 312329 (1958). MR0097227 (20 #3697) 23. M. Slemrod, "Dynamics of measure-valued solutions to a backward-forward parabolic equation," J. Dyn. Differ. Equ., 2, 128 (1991). MR1094722 (92m:35124)
Note: This list reflects references listed in the original paper as accurately as possible with no attempt to correct errors.

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MR3207073 (Review) 35R35 35A01 35J15 Selivanova, N. Yu. (RS-AOS-TI) ; Shamolin, M. V. [Shamolin, Maxim V.] (RS-MOSC-MC) Lo cal solvability of a one-phase problem with free b oundary. (English summary) Translated from Sovrem. Mat. Prilozh. No. 78 (2012). J. Math. Sci. (N. Y.) 189 (2013), no. 2, 274283.

Summary: "A certain one-phase problem with free b time) solvability of this problem is proved; moreover, applied in a more concrete case. For this purpose, a parametrization of the boundary are introduced, and a problem in a constant domain."
References

oundary is studied. The local (in the general method elaborated is new change of variables and the the problem studied is reduced to

1. I. I. Danilyuk, "On Stefan problem," Usp. Mat. Nauk, 40, No. 5(245), 133185 (1985). MR0810813 (87d:35003) 2. N. A. Eltysheva, "On qualitative properties of solutions of certain hyperbolic systems on the plane," Mat. Sb., 132, No. 2, 186209 (1988). 3. S. K. Godunov, Equations of Mathematical Physics [in Russian], Nauka, Moscow (1979). MR0548574 (80i:35001) 4. E. M. Kartashov, "Analytical methods for solving boundary-value problems of nonstationary heat conduction in domains with moving boundaries," Izv. Ross. Akad. Nauk, Ser. Energ., No. 5, 334 (1999). 5. M. M. Lavrent'ev (Jr) and N. A. Lyul'ko, "Enlarging smoothness of solutions of certain hyperbolic problems," Sib. Mat. Sh., 38, No. 1, 109124 (1997). MR1446678 (98b:35110) 6. M. Slemrod, "Dynamics of measure-valued solutions to a backward-forward parabolic equation," J. Dyn. Differ. Equ., 2, 128 (1991). MR1094722 (92m:35124) 7. S. L. Sobolev, "Locally nonequilibrium models of transport processes," Usp. Fiz. Nauk, 167, No. 10, 10951106 (1997).

8. A. D. Solomon, V. Alexiades, D. G. Wilson, and S. Drake, "On the formulation of hyperbolic Stefan problem," Quart. Appl. Math., 43, No. 3, 295304 (1985). MR0814228 (87c:80018) 9. Zh. O. Takhirov, "Two-phases problem with unknown boundaries for a first-order hyperbolic system of equations," Uzb. Mat. Zh., No. 6, 4856 (1991). MR1252617 (94i:35204) 10. A. N. Tikhonov and A. A. Samarskii, Equations of Mathematical Physics [in Russian], Nauka, Moscow (1977). 11. A. N. Tikhonov, A. V. Goncharskii, V. V. Stepanov, and A. G. Yagola, Numerical Methods for Solving Il l-Posed Problems [in Russian], Nauka, Moscow (1990). MR1126915 (92j:65113)
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MR3224103 (Review) 70E15 37J35 70G65 Shamolin, M. B. [Shamolin, Maxim V.] (RS-MOSC-IMC) A new case of integrability in transcendental functions in the dynamics of solid b o dy interacting with the environment. (English summary) Translation of Avtomat. i Telemekh. 2013, no. 8, 173190. Autom. Remote Control 74 (2013), no. 8, 13781392.

This paper concerns a problem in nonlinear rigid body mechanics. Starting from the 3D generalization of an integrable planar problem, the author considers a rigid body interacting with the environment by means of a resisting (quasi-stationary) force. The body is axially symmetric with a planar frontal butt in the form of a two-dimensional disc and the interaction is concentrated in this part. The main result contained in this paper is the determination of the full sets of first integrals for the problem under investigation. The interesting feature is that some of the first integral contains transcendental functions of dependent variables expressed in terms of a finite combination of the elementary functions. Giuseppe Saccomandi c Copyright American Mathematical Society 2015

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MR3185235 (Review) 37J35 70E15 70G65 Shamolin, M. V. [Shamolin, Maxim V.] (RS-AOS-MC) A new case of integrability in the dynamics of a multidimensional rigid b o dy in a nonconservative field. (Russian) Dokl. Akad. Nauk 453 (2013), no. 1, 4649.

The dynamics of a multidimensional rigid body described by an analogue of Euler and Newton equations on so(n) в Rn is considered. A new integrable case in this dynamics is described. Igor N. Nikitin c Copyright American Mathematical Society 2015

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MR3143879 (Review) 34C14 70E15 70G60 Shamolin, M. V. [Shamolin, Maxim V.] (RS-MOSC-MC) On integrability in dynamic problems for a rigid b o dy interacting with a medium. (English summary) Internat. Appl. Mech. 49 (2013), no. 6, 665674.

This paper addresses the computation of first integrals for the differential equations describing the dynamics of a homogeneous axisymmetric rigid body with a disk-shaped frontal area moving in a resisting medium. In particular, the author considers the motion of a body acted upon by a follower force which is directed along the geometrical symmetry axis of the body. Two cases of a constant follower force are treated in detail; in particular, first integrals, in terms of either elementary transcendental functions or analytic functions, are found. M. E. Sousa-Dias c Copyright American Mathematical Society 2015

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MR3059469 70E40 70E45 70G45 Shamolin, M. V. [Shamolin, Maxim V.] (RS-MOSC-NDM) A new integrability case of equations of dynamics on the tangent bundle of a 3-sphere. (Russian) Uspekhi Mat. Nauk 68 (2013), no. 5(413), 185186; translation in Russian Math. Surveys 68 (2013), no. 5, 963965.

References

1. M. B. ...M., 2007, 352 c. 2 M. B. ... PAH, 375:3 (2000), 343346. 3 M. B. ... 53:3(321) (1998), 209210. MR1657632 (99h:34006)

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MR3104009 (Review) 70E40 70E18 70E45 Shamolin, Maxim V. (RS-MOSC-MC) Variety of the cases of integrability in dynamics of a symmetric 2D-, 3D- and 4D-rigid b o dy in a nonconservative field. (English summary) Int. J. Struct. Stab. Dyn. 13 (2013), no. 7, 1340011, 14 pp.

The author considers the cases of integrability in dynamics of two- and three-dimensional rigid bodies in a nonconservative force field and develops the idea of generalisation of the equations to the case of a four-dimensional rigid body in an analogous nonconservative force field. As a result of this generalization, he obtains a variety of cases of integrability for the problem of body motion in a resisting medium that fills the four-dimensional space in the presence of a certain tracing force that allows one to reduce the order of the general system of ODE in a methodical way. A. E. Zakrzhevski i c Copyright American Mathematical Society 2015

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MR3114378 (Review) 70E45 70E40 Shamolin, M. V. [Shamolin, Maxim V.] (RS-MOSC-MC) A complete list of first integrals of the dynamic equations of motion of a fourdimensional rigid b o dy in a nonconservative field in the presence of linear damping. (Russian) Dokl. Akad. Nauk 449 (2013), no. 4, 416419.

A 4-dimensional homogeneous rigid body having a 2-dimensional disk as a flat front end face is considered. For the special case when the resistant force acting on the disk is concentrated on that part of the body surface that is shaped as a three-dimensional ball, the part of the equations of motion corresponding to the algebra so(4) is derived. In the case when the body has the dynamical symmetry property and an additional tracking force is applied, the complete list of nine invariant relations (first integrals) is given. Six of them are trivial and three others are transcendental functions in C which can be represented in the form of finite combinations of the elementary functions. A. S. Sumbatov c Copyright American Mathematical Society 2015

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MR3207058 (Review) 70E45 37J35 70E40 Shamolin, M. V. [Shamolin, Maxim V.] (RS-MOSC-MC) Comparison of complete integrability cases in dynamics of a two-, three-, and four-dimensional rigid b o dy in a nonconservative field. (English summary)

Translated from Sovrem. Mat. Prilozh., Vol. 76, 2012. J. Math. Sci. (N. Y.) 187 (2012), no. 3, 346359. In this paper the author investigates the Arnold-Liouville integrability for a dynamically symmetric four-dimensional rigid body having forward plane endwall which moves in a certain resistant media under action of non-conservative and tracing forces. Provided that the center mass of the body has always uniform rectilinear motion and that some quasi-stationary conditions take place, the complete set of first integrals is given for a plane-parallel motion of the body. The analogous results are obtained in the cases of three-dimensional space and, in the most complicated case concerned, the fourdimensional space of motion. It is proved that, in each case, one first integral is an analytic function of the phase variables and the other first integrals are transcendental (after the formal continuation to the complex domain). A. S. Sumbatov
References

1. O. I. Bogoyavlenskii, "Some integrable cases of Euler equations," Dokl. Akad. Nauk SSSR, 287, No. 5, 11051108 (1986). MR0839710 (87j:70005) 2. O. I. Bogoyavlenskii, "Dynamics of a rigid body with n ellipsoidal holes willed with a magnetic fluid," Dokl. Akad. Nauk SSSR, 272, No. 6, 13641367 (1983). MR0722875 (85e:58042) 3. D. V. Georgievskii and M. V. Shamolin, "Kinematics and mass geometry of a rigid body with fixed point in Rn ," Dokl. Ross. Akad. Nauk, 380, No. 1, 4750 (2001). MR1867984 (2003a:70002) 4. D. V. Georgievskii and M. V. Shamolin, "Generalized dynamical Euler equations for a rigid body with fixed point in Rn ," Dokl. Ross. Akad. Nauk, 383, No. 5, 635637 (2002). MR1930111 (2003g:70008) 5. D. V. Georgievskii and M. V. Shamolin, "First integrals of equations of motion of a generalized gyroscope in Rn ," Vestn. MGU, Ser. Mat., Mekh., 5, 3741 (2003). MR2042218 (2004j:70012) 6. D. V. Georgievskii and M. V. Shamolin, "Valerii Vladimirovich Trofimov," J. Math. Sci., 154, No. 4, 449461 (2008). MR2342521 7. S. V. Manakov, "A remark on integrating Euler equations of dynamics of an ndimensional rigid body," Funkts. Anal. Prilozh., 10, No. 4, 9394 (1976). MR0455031 (56 #13272) 8. S. P. Novikov and I. Shmel'tser, "Periodic solutions of Kirchhoff equation of free body motion in ideal fluid and extended LyusternikShnirel'manMorse theory (LMSh)," Funkts. Anal. Prilozh., 15, No. 3, 5466 (1981). MR0630339 (83a:58026a) 9. V. A. Samsonov and M. V. Shamolin, "On the problem of the motion of a body in a resisting medium," Vestn. MGU, Ser. Mat., Mekh., 3, 5154 (1989). MR1029730 (90k:70007) 10. M. V. Shamolin, "Problem of motion of a four-dimensional rigid body in a resisting medium and one integrability case," in: Proc. Third Int. Conf. "Differential Equations and Applications," Saint Petersburg, Russia, June 1217, 2000, St. Petersburg

Univ., St. Petersburg (2000), p. 198. 11. M. V. Shamolin, "Jacobi integrability of problem of a four-dimensional body motion in a resisting medium," in: Proc. Int. Conf. in Differential Equations and Dynamical Systems, Suzdal', August 2126, 2000 [in Russian], Vladimir State University, Vladimir (2000), pp. 196197. 12. M. V. Shamolin, "Comparison of some integrable cases from two-, three-, and four-dimensional rigid body dynamics interacting with a medium," in: Proc. of V Crimean Int. Math. School "Method of Lyapunov Functions and Its Applications," Alushta, September 519, 2000 [in Russian], Simferopol' (2000), p. 169. 13. M. V. Shamolin, "On a certain Jacobi integrability case in dynamics of a fourdimensional rigid body interacting with a medium," in: Proc. Int. Conf. in Differential and Integral Equations, Odessa, September 1214, 2000 [in Russian], AstroPrint, Odessa (2000), pp. 294295. 14. M. V. Shamolin, "Jacobi integrability in problem of a four-dimensional body motion in a resisting medium," Dokl. Ross. Akad. Nauk, 375, No. 3, 343346 (2000). MR1833828 (2002c:70005) 15. M. V. Shamolin, "New integrable cases in dynamics of a four-dimensional rigid body interacting with a medium," in: Proc. Conf. "Dynamical Systems Model ling and Stability Investigation," May 2225, 2001 [in Russian], Kyiv (2001), p. 344. 16. M. V. Shamolin, "New Jacobi integrable cases in dynamics of a two-, three-, and four-dimensional rigid body interacting with a medium," Proc. VIII Al l-Russian Congress in Theoretical and Applied mechanics, Perm', August 2329, 2001 [in Russian], Ekaterinburg (2001), pp. 599600. 17. M. V. Shamolin, "New integrable cases in dynamics of a two-, three-, and fourdimensional rigid body interacting with a medium," in: Proc. Int. Conf. in Differential Equations and Dynamical Systems, Suzdal', July 0106, 2002 [in Russian], Vladimir State Univ., Valadimir (2002), pp. 142144. 18. M. V. Shamolin, "On a certain integrable case in dynamics on so(4) в R4 ," in: Proc. Al l-Russian Conf. "Differential Equations and Their Applications," Samara, June 27--July 2, 2005 [in Russian], Samara (2005), pp. 9798. MR2225204 (2007a:70009) 19. M. V. Shamolin, "On a certain integrable case of dynamics equations on so(4) в R4 ," Usp. Mat. Nauk, 60, No. 6, 233234 (2005). MR2225204 (2007a:70009) 20. M. V. Shamolin, "On a complete integrability case in four-dimensional rigid body dynamics," in: Proc. Int. Conf. in Differential Equations and Dynamical Systems, Vladimir, July 1015, 2006 [in Russian], Vladimir State Univ., Vladimir (2006), pp. 226228. 21. M. V. Shamolin, "A complete integrability case in dynamics of a four-dimensional rigid body in a non-conservative force field," in: Proc. Int. Congr. "Nonlinear Dynamical Analysis," St. Petersburg, June 48, 2007 [in Russian], St. Petersburg State Univ., St. Petersburg (2007), p. 178. 22. M. V. Shamolin, "Complete integrability cases in dynamics of a four-dimensional rigid body in a non-conservative force field," in: Proc. Int. Conf. "Analysis and Singularities" Devoted to the 70th Birthday of V. I. Arnol'd, Moscow, August 2024, 2007 [in Russian], Steklov Math. Institute, Moscow (2007), pp. 110112. 23. M. V. Shamolin, Methods for Analysis of Variable Dissipation Dynamical Systems in Rigid Body Dynamics [in Russian], Ekzamen, Moscow (2007). 24. M. V. Shamolin, "New Jacobi integrable cases in dynamics of a rigid body interacting with a medium," Dokl. Ross. Akad. Nauk, 364, No. 5, 627629 (1999). MR1702618 (2000k:70008) 25. M. V. Shamolin, "On an integrable case in spatial dynamics of a rigid body interacting with a medium," Izv. Ross. Akad. Nauk, Mekh. Tv. Tela, 2, 6568 (1997).

26. M. V. Shamolin, "Methods of analysis of dynamics of a 2D-, 3D-, or 4D-rigid body with a medium," in: Proc. Int. Congr. Math., Beijing, August 2028, 2002, Higher Education Press, Beijing, China (2002), p. 268. 27. M. V. Shamolin, "4D rigid body and some cases of integrability," in: Proc. Int. Conf. Industr. Appl. Math., Zurich, Switzerland, June 1620, 2007, ETH Zurich (2007), p. 311. 28. M. V. Shamolin, "The cases of integrability in 2D-, 3D-, and 4D-rigid body," in: Proc. Int. Conf. "Dynamical Methods and Mathematical Model ling," Val ladolid, Spain, September 1822, 2007, ETSII, Valladolid (2007), p. 31. 29. V. V. Trofimov and A. T. Fomenko, Algebra and Geometry of Integrable Hamiltonian Differential Equations [in Russian], Faktorial, Moscow (1995). MR1469742 (98f:58118) 30. V. V. Trofimov and A. T. Fomenko, "Geometry of Poisson brackets and Liouville integration methods of systems on symmetric spaces," in: Progress in Science and Technology, Series on Contemporary Problems in Mathematics [in Russian], 29, All-Union Institute for Scientific and Technical Information, USSR Academy of Sciences, Moscow (1986), pp. 380. MR0892743 (88i:58059) 31. A. P. Veselov, "LandauLifshits equation and integrable systems of classical mechanics," Dokl. Akad. Nauk SSSR, 270, No. 5, 10941097 (1983). MR0714061 (85c:58055) 32. A. P. Veselov, "On integrability conditions for Euler equations on so(4)," Dokl. Akad. Nauk SSSR, 270, No. 6, 12981300 (1983). MR0712935 (84m:58062)
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MR3207055 (Review) 70E15 37J35 70G45 Georgievskii, D. V. [Georgievskii, Dimitri V.] (RS-MOSC-MM) ; Shamolin, M. V. [Shamolin, Maxim V.] (RS-MOSC-MC) Levi-Civita symb ols, generalized vector pro ducts, and new integrable cases in mechanics of multidimensional b o dies.

Translated from Sovrem. Mat. Prilozh., Vol. 76, 2012. J. Math. Sci. (N. Y.) 187 (2012), no. 3, 280299. Two new cases of completely integrable dynamics of a 4-dimensional rigid body in a non-conservative force field of a special form are presented. Igor N. Nikitin
References

1. W. Blaschke, "Nicht-Euklidische Geometrie und Mechanik," Math. Einrelshriften. Hamburg, 34, 39 (1942). MR0009861 (5,215b) 2. O. I. Bogoyavlenskii, "Some integrable cases of Euler equations," Dokl. Akad. Nauk SSSR, 287, No. 5, 11051108 (1986). MR0839710 (87j:70005) 3. O. I. Bogoyavlenskii, "Dynamics of a rigid body with n ellipsoidal holes filled with a magnetic fluid," Dokl. Akad. Nauk SSSR, 272, No. 6, 13641367 (1983). MR0722875

(85e:58042) 4. O. V. Bogoyavlenskii, Overturning Solitons [in Russian], Nauka, Moscow (1991). MR1261186 (95e:58077) 5. O. Bottema and H. J. E. Beth, "Euler's equations for the motion of a rigid body in an n-dimensional space," Indag. Math., 13, No. 1, 106108 (1951). MR0040861 (12,759i) 6. B. A. Dubrovin, I. M. Krichiver, and S. P. Novikov, "Integrable systems, I," in: Progress in Science and Technology, Series on Contemporary Problems in Mathematics, Fundamental Directions [in Russian], 4, All-Union Institute for Scientific and Technical Information, USSR Academy of Sciences, Moscow (1985), pp. 179285. MR0842910 (87k:58112) Ё 7. W. von Frahm, "Uber gewisse Differentialgleichungen," Math. Ann., 8, 3544 (1874). 8. D. V. Georgievskii, "Structure of polynomial solutions to system of equations of elasticity theory in stresses," Izv. Ross. Akad. Nauk., Mekh. Tv. Tela, 5, 4451 (2008). 9. D. V. Georgievskii and B. E. Pobedrya, "On the number of independent compatibility equations in deformable rigid body mechanics," Prikl. Mat. Mekh., 68, No. 6, 10431048 (2004). MR2125034 (2005m:74008) 10. D. V. Georgievskii and M. V. Shamolin, "Kinematics and mass geometry odf a rigid body with fixed point in Rn ," Dokl. Ross. Akad. Nauk, 380, No. 1, 4750 (2001). MR1867984 (2003a:70002) 11. D. V. Georgievskii and M. V. Shamolin, "Generalized dynamical Euler equations for a rigid body with a fixed point in Rn ," Dokl. Ross. Akad. Nauk, 383, No. 5, 635637 (2002). MR1930111 (2003g:70008) 12. D. V. Georgievskii and M. V. Shamolin, "First integrals of equations of motion of generalized gyroscope in Rn ," Vestn. MGU, Ser. 1, Mat., Mekh., 5, 3741 (2003). MR2042218 (2004j:70012) 13. V. I. Gorbachev and A. L. Mikhailov, "Stress concentration tensor for the case of an N -dimensional elastic space with spherical inclusion," Vestn. MGU, Ser. 1, Mat., Mekh., 2, 7883 (1993). 14. E. KrЁ oner, Al lgemeine Kontinuumstheorie der Versetzungen und Eigenspannungen, Springer-Verlag, Berlin (1958). MR0095615 (20 #2117) 15. I. A. Kunin, "Dislocation theory," in: J. A. Schouten, Tensor Analysis for Physicists [Russian translation], Nauka, Moscow (1965), pp. 373443. 16. S. V. Manakov, "A note on integrating equations of dynamics of an n-dimensional rigid body," Funkts. Anal. Prilozh., 10, No. 4, 9394 (1976). MR0455031 (56 #13272) 17. A. S. Mishchenko, "Integrals of geodesic flows on Lie groups," Funkts. Anal. Prilozh., 4, No. 3, 7378 (1970). MR0274891 (43 #649) 18. Z. Nitecki, Introduction to Differential Dynamics [Russian translation], Mir, Moscow (1975). MR0649789 (58 #31211) 19. S. P. Novikov and I. Shmel'tser, "Periodic solutions of Kirchhoff equation of free body motion in ideal fluid and extended LyusternikShnirel'manMorse theory (LMSh)," Funkts. Anal. Prilozh., 15, No. 3, 5466 (1981). MR0630339 (83a:58026a) 20. B. E. Pobedrya and D. V. Georgievskii, Foundations of Continuum Medium Mechanics [in Russian], Fizmatlit, Moscow (2006). 21. B. E. Pobedrya and D. V. Georgievskii, "Equivalence of formulations for problems in elasticity theory in terms of stresses," Russ. J. Math. Phys., 13, No. 2, 203209 (2006). MR2262824 (2007e:74007) 22. V. A. Samsonov and M. V. Shamolin, "On the problem of body motion in a

23.

24. 25. 26.

27. 28.

29. 30.

resisting medium," Vestn. MGU, Ser. 1, Mat., Mekh., 3, 5154 (1989). MR1029730 (90k:70007) M. V. Shamolin, "New Jacobi integrable cases in dynamics of a rigid body interacting with a medium," Dokl. Ross. Akad. Nauk, 364, No. 5, 627629 (1999). MR1702618 (2000k:70008) M. V. Shamolin, "On an integrable case in spatial dynamics of a rigid body interacting with a medium," Izv. Ross. Akad. Nauk, Mekh. Tv. Tela, 2, 6568 (1997). M. V. Shamolin, Methods for Analyzing Variable Dissipation Dynamical Systems in Rigid Body Dynamics [in Russian], Ekzamen, Moscow (2007). V. V. Trofimov and A. T. Fomenko, "Poisson bracket geometry and methods for Liouville integration of systems on symmetric spaces," in: Progress in Science and Technology, Series on Contemporary Problems in Mathematics [in Russian], 29, All-Union Institute for Scientific and Technical Information, USSR Academy of Sciences, Moscow (1986), pp. 380. MR0892743 (88i:58059) V. V. Trofimov and A. T. Fomenko, Algebra and Geometry of Integrable Hamiltonian Systems [in Russian], Faktorial, Moscow (1995). MR1469742 (98f:58118) A. P. Veselov, "LandauLifshits equation and integrable systems of classical mechanics," Dokl. Akad. Nauk SSSR, 270, No. 5, 10941097 (1983). MR0714061 (85c:58055) A. P. Veselov, "On integrability conditions of Euler equations on so(4)," Dokl. Akad. Nauk SSSR, 270, No. 6, 12981300 (1983). MR0712935 (84m:58062) H. Weyl, Raum, Zeit, Materie, Springer, Berlin (1923). MR0988402 (90a:01111)
Note: This list reflects references listed in the original paper as accurately as possible with no attempt to correct errors.

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MR3099806 70E15 Shamolin, M. V. (RS-MOSC-NDM) The problem of the motion of a b o dy in a resisting medium taking into account the dep endence of the force moment of resistance on the angular momentum. (Russian. English, Russian summaries) Mat. Model. 24 (2012), no. 10, 109132.

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MR3027135 (Review) 70E45 Shamolin, M. V. (RS-MOSC-IMC) A new integrability case in the dynamics of a four-dimensional rigid b o dy in a nonconservative field under linear damping. (Russian) Dokl. Akad. Nauk 444 (2012), no. 5, 506509.

The paper deals with the dynamics of a four-dimensional rigid body described by the system of differential equations + + [, + ] = M , where so(4) is the matrix of the angular velocity, while = diag(1 , . . . , 4 ) is the inertia tensor, i = 1 (I1 + I2 + I3 + I4 ) - Ii . The main difference from the previously 2 studied integrable cases is the presence of non-conservative external forces entering into the equations of motion through the matrix of the external momentum M . In the highly symmetric case I2 = I3 = I4 , the author gives a (rather complicated and artificial) choice of the momentum M depending linearly on , which ensures the existence of a full set of integrals of motion. Yuri B. Suris c Copyright American Mathematical Society 2015

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MR3027120 (Review) 70E15 Shamolin, M. V. (RS-MOSC-IMC) A complete list of first integrals for the dynamic equations of motion of a rigid b o dy in a resisting medium taking into account linear damping. (Russian. English, Russian summaries) Vestnik Moskov. Univ. Ser. I Mat. Mekh. 2012, no. 4, 4447.

The present paper considers a new case of integrability in the problem of spatial rigid body motion in the presence of a nonconservative moment of forces. A nonconservative force field of action of the medium on the body is constructed taking into account the linear dependence of the field on the angular velocity. Clementina D. Mladenova c Copyright American Mathematical Society 2015

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MR2963695 70E15 70G60 Shamolin, M. V. (RS-MOSC-MC) A new integrability case in the spatial dynamics of a rigid b o dy interacting with a medium taking linear damping into account. (Russian) Dokl. Akad. Nauk 442 (2012), no. 4, 479481.

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MR2964370 (Review) 70E15 70K40 Shamolin, M. V. (RS-MOSC-IMC) Motion of a rigid b o dy in a resisting medium. (Russian. English, Russian summaries) Mat. Model. 23 (2011), no. 12, 79104.

This paper deals with the plane-parallel motion of a rigid body interacting with a homogeneous stream of a resisting medium only through a forward flat site of its surface. The motion of the resisting medium is not studied. Gravity is considered to be small in comparison with the force of action of the medium. The considered model corresponds to a problem about putting homogeneous circular cylinders in water. The force action of the medium is defined on the basis of experimental data. The mathematical model for the problem is reduced to the equations of plane-parallel motion of a rigid body. The problem's generalized coordinates are defined by the velocity vector and the magnitude of the angular velocity of the body. The force action of the medium is considered in the framework of a linearized model. The main ob jective of the research consists in studying the effect of the torque of the force of action of a medium. Further, conditions of the asymptotic stability of rectilinear translational braking are investigated. A multiparameter set of phase portraits in the space of quasivelocities is obtained. Separately the problem about putting a hollow cylinder in water is considered with the ob jective of defining relations of its mass-geometrical parameters, which would ensure the stability of the braking of a translational motion of such a cylinder in water. At the end of the paper, the author adduces reasons concerning features of carrying out natural experiments. A. E. Zakrzhevski i c Copyright American Mathematical Society 2015

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MR2919134 (Review) 70E45 70E40 70G45 Shamolin, M. V. (RS-MOSC-IMC) A complete list of first integrals in the problem of the motion of a fourdimensional b o dy in a nonconservative field under linear damping. (Russian) Dokl. Akad. Nauk 440 (2011), no. 2, 187190.

The motion of a four-dimensional rigid body in a nonconservative field is considered. This study is a continuation of previous investigations of the author in lower dimensions. Under certain assumptions on the nature of the nonconservative field, the equations of motion of the rigid body are derived and then analyzed. For the dynamically symmetric rigid body a complete list of first integrals is given. Thereby, a new integrable case is found. O. Christov c Copyright American Mathematical Society 2015

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MR2918863 (Review) 70E15 70K05 Shamolin, M. V. (RS-MOSC-IMC) A multiparameter family of phase p ortraits in the dynamics of a rigid b o dy interacting with a medium. (Russian. English, Russian summaries) Vestnik Moskov. Univ. Ser. I Mat. Mekh. 2011, no. 3, 2430.

The author considers the plane-parallel motion of a homogeneous symmetric rigid body interacting with a medium only through a flat region of its outer surface. The force field acting on the body is constructed from information on the properties of jet flow under quasistationary conditions. The motion of the medium is not considered and the weight of the body is also ignored. The motion of the body dynamics is studied for the case when the characteristic time of motion of the body relative to its center of mass is comparable with the characteristic time of the mass center. The effects of moments acting on the body are taken into account. The second part of the article is devoted to a classification of the phase portraits which are based upon the analysis of the differential equations of motion. The main goal of the phase portrait classification is to study the behavior of stable and unstable separatrices of hyperbolic saddles. It is shown that any sufficiently small perturbation of a system describing a physical pendulum changes the global type of the unperturbed phase portrait (these changes occur infinitely many times). B. Vujanoviґ c c Copyright American Mathematical Society 2015

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MR2849353 70H06 37N05 70G65 Shamolin, M. V. (RS-MOSC-IMC) A new case of integrability in the dynamics of a four-dimensional rigid b o dy in a nonconservative field. (Russian) Dokl. Akad. Nauk 437 (2011), no. 2, 190193.

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MR2923140 (Review) 70E15 70K40 Shamolin, M. V. (RS-MOSC-MC) Spatial motion of a rigid b o dy in a resisting medium. (English summary) Internat. Appl. Mech. 46 (2010), no. 7, 835846.

Summary: "The paper studies the spatial motion of a rigid body in a resisting medium under the action of a follower force that causes the center of mass to move rectilinearly and uniformly. The body, which is axisymmetric and homogeneous, interacts with the medium by its frontal area that has the form of a flat circular disk. Since there is no exact analytic description of the forces and torques exerted by the medium on the disk, the problem is `immersed' in a wider class of problems. Partial solutions and phase portraits in the three-dimensional space of quasivelocities are obtained for the dynamic systems under consideration. The transcendental first integrals of the dynamic part of the equations of motion are listed." c Copyright American Mathematical Society 2015

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MR2786542 (2012k:37123) 37J35 37N05 70H06 Trofimov, V. V. (RS-MOSC) ; Shamolin, M. V. (RS-MOSC) Geometric and dynamical invariants of integrable Hamiltonian and dissipative systems.2076-6203 (Russian. English, Russian summaries) Fundam. Prikl. Mat. 16 (2010), no. 4, 3229; translation in J. Math. Sci. (N. Y.) 180

(2012), no. 4, 365530. This paper is related to the two D.Sc. theses of the authors on various aspects of the dynamics of integrable systems. The first part of the paper is based on research carried out by Trofimov. In the first chapter a method for constructing completely integrable Hamiltonian systems on the coadjoint representation of Lie groups is proposed. Within this method new examples of completely integrable systems are constructed. This method makes it

possible to prove the complete integrability of the equations, previously known as a multidimensional extension of the equations of magnetohydrodynamics. A theorem on the complete integrability of the Euler equations on tensor extensions of semisimple Lie algebras is proved. The second chapter is devoted to a geometric construction allowing one to classify Hamiltonian systems with first integrals. The construction mentioned is based on the extension of the Maslov class concept. Completely integrable systems with nontrivial generalized Maslov classes on the coadjoint orbits of Lie groups of small dimension are explored in Chapter 3. The second part of the book is based on research carried out by Shamolin. Some classes of completely integrable non-conservative systems are investigated in Chapter 4. Systems under the action of non-conservative forces and variable dissipation are considered in Chapter 5. A system possessing a first integral which is a transcendental function of phase variables is pointed out. Some examples related to rigid body dynamics under the action of non-conservative forces are studied. Invariant indices characterizing countable sets of phase portraits are discussed. In Chapter 6, cases of the complete integrability of a four-dimensional dynamically symmetric top moving under the action Alexander Burov of non-conservative forces are indicated.
References

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MR2759285 (2012a:65053) 65D30 A idagulov, R. R. (RS-MOSC-IMC) ; Shamolin, M. V. (RS-MOSC-IMC) Integration formulas of the tenth order of accuracy and higher. (Russian. English, Russian summaries) Vestnik Moskov. Univ. Ser. I Mat. Mekh. 2010, no. 4, 37; translation in Moscow Univ. Math. Bul l. 65 (2010), no. 4, 135139.

Summary: "Nowadays, due to the considerable growth of computer capacity, the development of more efficient quadrature formulas may seem unnecessary. However, if the calculation of each integrand value requires much computational time or we have to study the dependence of the integral on a large number of parameters the integrand is determined through, then it is necessary to use more efficient formulas." c Copyright American Mathematical Society 2012, 2015

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MR2682718 (2012a:70010) 70E40 70H06 Shamolin, M. V. (RS-MOSC-IMC) New integrability cases in the three-dimensional dynamics of a rigid b o dy. (Russian) Dokl. Akad. Nauk 431 (2010), no. 3, 339343.

From the text (translated from the Russian): "The results of this paper are based on an investigation of ours of a problem of the motion of a rigid body in a resisting medium [Methods for the analysis of dynamical systems with variable dissipation in the ` dynamics of a rigid body (Russian), Ekzamen, Moscow, 2007; Fundam. Prikl. Mat. 14 (2008), no. 3, 3237; MR2482029 (2010f:37032)], where we dealt with first integrals

of dynamical systems with nonstandard properties. Specifically, the integrals were neither analytical nor smooth, and for certain sets, they were even discontinuous. These properties allowed us to thoroughly analyze all phase tra jectories and to indicate the properties that possessed `structural stability' and were preserved for systems of more general form with certain nontrivial symmetries of hidden type. Therefore, it is of interest to investigate a sufficiently large class of systems with similar properties, in particular, those involving the dynamics of a rigid body interacting with a medium. In this paper, we present new integrability cases in the problem of the three-dimensional dynamics of a rigid body in a resisting medium." c Copyright American Mathematical Society 2012, 2015

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MR2655252 (2011e:70008) 70E40 34A05 37J35 70E45 70H06 Shamolin, M. V. (RS-MOSC-MC) The case of complete integrability in the dynamics of a four-dimensional rigid b o dy in a nonconservative field. (Russian) Uspekhi Mat. Nauk 65 (2010), no. 1(391), 189190; translation in Russian Math. Surveys 65 (2010), no. 1, 183185.

From the text (translated from the Russian): "We continue our search for new integrable cases in the dynamics of a four-dimensional rigid body in R4 в so(4) in a nonconservative force field [M. V. Shamolin, Dokl. Akad. Nauk 375 (2000), no. 3, 343346; MR1833828 i (2002c:70005); D. V. Georgievski and M. V. Shamolin, Dokl. Akad. Nauk 380 (2001), no. 1, 4750; MR1867984 (2003a:70002); M. V. Shamolin, Methods for the analysis of dynamical systems with variable dissipation in the dynamics of a rigid body (Russian), ` Izdat. "Ekzamen", Moscow, 2007; per bibl.]. Earlier, we presented the case of complete integrability of the equations of motion of a dynamically symmetric body when I1 = I2 = I3 = I4 [op. cit., 2000]. In the present paper, we thoroughly analyze the case of another logically possible dynamic symmetry."
References

1. ..., ... 375:3 (2000), 343346; English transl., M. V. Shamolin, Dokl. Phys. 45:11 (2000), 632634. MR1833828 (2002c:70005) 2. ..., ..., ... 380:1 (2001), 4750; English transl., D. V. Georgievskii and M. V. Shamolin, Dokl. Phys. 45:9 (2001), 663666. 3. ..., .... 2007. [M. V. Shamolin, Methods of analysis of dynamical systems with varable dissipation in rigid body dynamics, `Ekzamen', Moscow 2007.] 4. ..., ..., ..., .... 1979; English transl., B. A. Dubrovin, A. T. Fomenko, and S. P. Novikov, Modern geometrymethods and applications. Part I. The geometry of surfaces, transformation groups, and fields, Graduate Texts in Math., vol. 93, Springer-Verlag, New York 1984; Modern geometrymethods and applications. Part II. The geometry and topology of manifolds, Graduate Texts in Math., vol. 104, Springer-Verlag, New York 1985; Modern geometrymethods and applications. Part III. Introduction to homology theory, Graduate Texts in Math., vol. 124, Springer-Verlag, New York 1990. MR0736837 (85a:53003)

5. ..., ...., 1984, no. 6, 3133; English transl., V. V. Trofimov, Mosc. Univ. Math. Bul l. 39:6 (1984), 4447. 6. ..., ... 287:5 (1986), 11051109; English transl., O. I. Bogoyavlenskii, Soviet Phys. Dokl. 31:3 (1986), 309311. MR0839710 (87j:70005) 7. ..., ... 364:5 (1999), 627629; English transl., M. V. Shamolin, Dokl. Phys. 44:2 (1999), 110113. MR1702618 (2000k:70008) 8. ..., ... 53:3 (1998), 209210; English transl., M. V. Shamolin, Russian Math. Surveys 53:3 (1998), 637638. MR1657632 (99h:34006)
Note: This list reflects references listed in the original paper as accurately as possible with no attempt to correct errors.

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MR2916243 (Review) 70E15 Shamolin, M. V. (RS-MOSC-MC) Stability of a rigid b o dy translating in a resisting medium. (English summary) Internat. Appl. Mech. 45 (2009), no. 6, 680692.

Summary: "The paper discusses a nonlinear model that describes the interaction of a rigid body with a medium and takes into account (based on experimental data on the motion of circular cylinders in water) the dependence of the arm of the force on the normalized angular velocity of the body and the dependence of the moment of the force on the angle of attack. An analysis of plane and spatial models (in the presence or absence of an additional follower force) leads to sufficient stability conditions for translational motion, as one of the key types of motions. Either stable or unstable self-oscillation can be observed under certain conditions." c Copyright American Mathematical Society 2015

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MR2828400 (2012e:70013) 70E45 70E15 70H06 Shamolin, M. V. (RS-MOSC-MC) Classification of complete integrability cases in the dynamics of a symmetric four-dimensional rigid b o dy in a nonconservative field. (Russian. Russian summary)

Sovrem. Mat. Prilozh. No. 65, Matematicheskaya Fizika, Kombinatorika i Optimal noe Upravlenie (2009), 131141; translation in J. Math. Sci. (N. Y.) 165 (2010), no. 6, 743754. Summary (translated from the Russian): "This paper is a relatively final result in the investigation of the equations of motion of a dynamically symmetric four-dimensional

rigid body in two logically possible cases of its tensor of inertia in a nonconservative force field. The form of the force field considered is taken from the dynamics of real three-dimensional rigid bodies interacting with a medium."
References

1. S. A. Agafonov, D. V. Georgievskii, and M. V. Shamolin, "Certain topical problems of geometry and mechanics," In: Abstracts of Sessions of the Workshop "Topical Problems of Geometry and Mechanics," Contemporary Mathematics. Fundamental Directions [in Russian], 23 (2007), p. 34. 2. O. I. Bogoyavlenskii, "Some integrable cases of Euler equations," Dokl. Akad. Nauk SSSR, 287, No. 5, 11051108 (1986). MR0839710 (87j:70005) 3. O. I. Bogoyavlenskii, "Dynamics of a rigid body with n ellipsoidal holes filled with a magnetic fluid," Dokl. Akad. Nauk SSSR, 272, No. 6, 13641367 (1983). MR0722875 (85e:58042) 4. D. V. Georgievskii and M. V. Shamolin, "On kinematics of a rigid body with fixed point in Rn ," In: Abstracts of Sessions of the Workshop "Topical Problems of Geometry and Mechanics," Fund. Prikl. Mat. [in Russian], 7, No. 1 (2001), p. 315. 5. D. V. Georievskii and M. V. Shamolin, "Kinematics and mass geometry of a rigid body with a fixed point in Rn ," Dokl. Ross. Akad. Nauk, 380, No. 1, 4750 (2001). MR1867984 (2003a:70002) 6. D. V. Georgievskii and M. V. Shamolin, "Generalized dynamical Euler equations for a rigid body with fixed point in Rn ," Dokl. Ross. Akad. Nauk, 383, No. 5, 635637 (2002). MR1930111 (2003g:70008) 7. D. V. Georgievskii and M. V. Shamolin, "First integrals of equations of motion of a generalized gyroscope in Rn ," Vestn. MGU, Mat., Mekh., No. 5, 3741 (2003). MR2042218 (2004j:70012) 8. D. V. Georgievskii and M. V. Shamolin, "Valerii Vladimirovich Trofimov," In: Abstracts of Sessions of the Workshop "Topical Problems of Geometry and Mechanics," Contemporary Mathematics. Fundamental Directions [in Russian], 23 (2007), pp. 56. MR2342521 9. D. V. Georgievskii and M. V. Shamolin, "On kinematics of a rigid body with fixed point in Rn ," In: Abstracts of Sessions of the Workshop "Topical Problems of Geometry and Mechanics," Contemporary Mathematics. Fundamental Directions [in Russian], 23 (2007), pp. 2425. 10. D. V. Georgievskii and M. V. Shamolin, "Generalized dynamical Euler equations for a rigid body with fixed point in Rn ," In: Abstracts of Sessions of the Workshop "Topical Problems of Geometry and Mechanics," Contemporary Mathematics. Fundamantal Directions [in Russian], 23 (2007), p. 30. 11. D. V. Georgievskii and M. V. Shamolin, "First integrals of equations of motion of a generalized gyroscope in n-dimensional space," In: Abstracts of Sessions of the Workshop "Topical Problems of Geometry and Mechanics," Contemporary Mathematics. Fundamental Directions [in Russian], 23 (2007), p. 31. 12. D. V. Georgievskii, V. V. Trofimov, and M. V. Shamolin, "Geometry and mechanics: Problems, approaches, and methods," In: Abstracts of Sessions of the Workshop "Topical Problems of Geometry and Mechanics," Fund. Prikl. Mat. [in Russian], 7, No. 1 (2001), p. 301. 13. D. V. Georgievskii, V. V. Trofimov, and M. V. Shamolin, "Geometry and mechanics: Problems, approaches, and methods," In: Abstracts of Sessions of the Workshop "Topical Problems of Geometry and Mechanics," Contemporary Mathematics. Fundamental, Directions [in Russian], 23 (2007), p. 16.

14. S. V. Manakov, "A note on integration of Euler equations of n-dimensional rigid body dynamics," Funkts. Anal. Pril., 10, No. 4, 9394 (1976). MR0455031 (56 #13272) 15. S. P. Novikov and I. Shmel'tser, "Periodic solutions of Kirchhoff equations of free motion of a rigid body and an ideal fluid and the extended Lyusternik-Shnirel'manMorse (LSM) theory. I," Funkts. Anal. Pril., 15, No. 3, 5466 (1981). MR0630339 (83a:58026a) 16. V. A. Samsonov and M. V. Shamolin, "On the problem of body motion in a resisting medium," Vestn. MGU, Mat., Mekh., 3, 5154 (1989). MR1029730 (90k:70007) 17. M. V. Shamolin, Methods for Analyzing Dynamical Systems with Variable Dissipation in Rigid-Body Dynamics [in Russian], Examen, Moscow (2007). 18. M. V. Shamolin, "New Jacobi integrable cases in dynamics of a rigid body interacting with a medium," Dokl. Ross. Akad. Nauk, 364, No. 5, 627629 (1999). MR1702618 (2000k:70008) 19. M. V. Shamolin, "On an integrable case in spatial dynamics of a rigid body interacting with a medium," Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, 2, 6568 (1997). 20. M. V. Shamolin, "The problem of four-dimensional rigid body motion in a resisting medium and one integrability case," In: Book of Abs. Third Int. Conf. "Differential Equations and Applications," St. Petersburg, Russia, June 1217, 2000 [in Russian]; StPbGTU, St. Petersburg (2000), p. 198. 21. M. V. Shamolin, "Jacobi integrability of the problem of four-dimensional rigid body motion in a resisting medium," In: Abstracts of Reports of the International Conference on Differential Equations and Dynamical Systems (Suzdal', 2126.08.2000) [in Russian], Vladimir State University, Vladimir (2000), pp. 196197. 22. M. V. Shamolin, "Comparison of certain integrable cases from two-, three-, and fourdimensional dynamics of a rigid body interacting with a medium," In: Abstracts of Reports of the Vth Crimean International Mathematical School "Lyapunov Function Method and Its Applications" (MFL-2000) (Crimea, Alushta, 0513.09.2000) [in Russian], Simferopol (2000), p. 169. 23. M. V. Shamolin, "On a certain Jacobi integrability case in the dynamics of a fourdimensional rigid body interacting with a medium," In: Abstracts of Reports of the International Conference on Differential and Integral Equations (Odessa, 12 14.09.2000) [in Russian], AstroPrint, Odessa (2000), pp. 294295. 24. M. V. Shamolin, "Jacobi integrability in the problem of four-dimensional rigid-body motion in a resisting medium," Dokl. Ross. Akad. Nauk, 375, No. 3, 343346 (2000). MR1833828 (2002c:70005) 25. M. V. Shamolin, "Integrability of the problem of four-dimensional rigid-body motion in a resisting medium," In: Abstracts of Sessions of the Workshop "Topical Problems of Geometry and Mechanics," Fund. Prikl. Mat. [in Russian], 7, No. 1 (2001), p. 309. 26. M. V. Shamolin, "New integrable cases in the dynamics of a four-dimensional rigid body interacting with a medium," In: Dynamical Systems Modeling and Stability Investigation. Scientific Conference (2225.5.2001), Abstracts of Conference Reports, Kiev (2001), p. 344. 27. M. V. Shamolin, "New Jacobi integrable cases in the dynamics of a two-, three-, and four-dimensional rigid body interacting with a medium," In: Abstracts of Reports of the VIIIth Al l-Russian Session in Theoretical and Applied Mechanics (Perm', 23 29.08.2001) [in Russian], Ural Department of the Russian Academy of Sciences, Ekaterinburg (2001), pp. 599600. 28. M. V. Shamolin, "New integrable cases in the dynamics of a two-, three-, and

29.

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four-dimensional rigid body interacting with a medium," In: Abstracts of Reports of the International Conference on Differential Equations and Dynamical Systems (Suzdal', 0106.07.2002) [in Russian], Vladimir State University, Vladimir (2002), pp. 142144. M. V. Shamolin, "On a certain integrable case in dynamics on so(4) в R4 ," In: Abstracts of Reports of the Al l-Russian Conference "Differential Equations and Their Applications" (SamDif 2005), Samara, June 27-July 2, 2005 [in Russian], Univers-grup, Samara (2005), pp. 9798. M. V. Shamolin, "On a certain integrable case of dynamics equations on so(4) в Rn ," Usp. Mat. Nauk, 60, No. 6, 233234 (2005). MR2225204 (2007a:70009) M. V. Shamolin, "On a case of complete integrability in the dynamics of a fourdimensional rigid body," In: Abstracts of Reports on Differential Equations and Dynamical Systems, Vladimir, 1015.07.2006 [in Russian], Vladimir State University, Vladimir (2006), pp. 226228. M. V. Shamolin, "Integrability of the problem of four-dimensional rigid-body motion in a resisting medium," In: Abstracts of Sessions of the Workshop "Topical Problems of Geometry and Mechanics," Contemporary Mathematics. Fundamental Directions [in Russian], 23 (2007), p. 21. M. V. Shamolin, "New integrable cases in the dynamics of a four-dimensional rigid body interacting with a medium," In: Abstracts of Sessions of the Workshop "Topical Problems of Geometry and Mechanics," Contemporary Mathematics. Fundamental Directions [in Russian], 23 (2007), p. 27. M. V. Shamolin, "On integrability of motion of a four-dimensional rigid body, a pendulum, being in over-run medium flow," In: Abstracts of Sessions of the Workshop "Topical Problems of Geometry and Mechanics," Contemporary Mathematics. Fundamental Directions [in Russian], 23 (2007), p. 37. M. V. Shamolin, "A case of complete integrability in the dynamics of a fourdimensional rigid body in a nonconservative force field," In: Abstracts of Reports of the International Congress "Nonlinear Dynamical Analysis-2007," St. Petersburg, June 4 8, 2007 [in Russian], St. Petersburg State University, St. Petersburg (2007), p. 178. M. V. Shamolin, "Case of complete integrability in the dynamics of a fourdimensional rigid body in a nonconsevative force field," In: Abstracts of Reports of the International Conference "Analysis and Singularities," Devoted to the 70th Anniversary of V. I. Arnol'd, Moscow, August 2024, 2007 [in Russian], MIAN, Moscow (2007), pp. 110112. M. V. Shamolin, "Methods of analysis of dynamics of a 2D- 3D- or 4D-rigid body with a medium," In: Abstr. Short Commun. Post Sess. of ICM'2002, Beijing, 2002, August 2028, Higher Education Press, Beijing, China (2002), p. 268. M. V. Shamolin, "4D rigid body and some cases of integrability," In: Abstracts of ICIAM07, Zurich, Switzerland, June 1620, 2007, ETH Zurich (2007), p. 311. M. V. Shamolin, "Cases of integrability in 2D-, 3D- and 4D-rigid body," In: Abstr. of Brief Commun. and Post. of Int. Conf. "Dynamical Methods and Mathematical Modeling," Val ladolid, Spane (Sept. 1822, 2007), ETSII, Valladolid (2007), p. 31. V. V. Trofimov and A. T. Fomenko, "Geometry of Poisson brackets and methods for Liouville integration of systems on symmetric spaces," In: Progress in Science and Technology, Series on Contemporary Problems in Mathematics [in Russian], 29, All-Union Institute for Scientific and Technical Information, USSR Academy of Sciences, Moscow, (1986), pp. 380. MR0892743 (88i:58059) A. P. Veselov, "Landau-Lifshits equation and integrable systems of classical mechanics," Dokl. Akad. Nauk SSSR, 270, No. 5, 10941097 (1983). MR0714061 (85c:58055)

42. A. P. Veselov, "On integrability conditions for Euler equations on so(4)," Dokl. Akad. Nauk SSSR, 270, No. 6, 12981300 (1983). MR0712935 (84m:58062)
Note: This list reflects references listed in the original paper as accurately as possible with no attempt to correct errors.

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MR2828399 34A05 Okunev, Yu. M. (RS-MOSC-MC) ; Shamolin, M. V. (RS-MOSC-MC) On the integrability in elementary functions of some classes of complex nonautonomous equations. (Russian. Russian summary)

Sovrem. Mat. Prilozh. No. 65, Matematicheskaya Fizika, Kombinatorika i Optimal noe Upravlenie (2009), 121130; translation in J. Math. Sci. (N. Y.) 165 (2010), no. 6, 732742.

References

1. A. A. Andronov, A Col lection of Works [in Russian], Akad. Nauk SSSR, Moscow (1956). 2. A. A. Andronov and L. S. Pontryagin. "Rough systems," Dokl. Akad. Nauk SSSR, 14, No. 5, 247250 (1937). 3. A. A. Andronov, A. A. Witt, and S. E. Khaikin. Oscil lation Theory [in Russian], Nauka, Moscow (1981). 4. A. A. Andronov, E. A. Leontovich, I. I. Gordon, and A. G. Maier, Qualitative Theory of Second-Order Dynamical Systems [in Russian], Nauka, Moscow (1966). MR0199506 (33 #7650) 5. A. A. Andronov, E. A. Leontovich, I. I. Gordon, and A. G. Maier, Bifurcation Theory of Dynamical Systems on a Plane [in Russian], Nauka, Moscow (1967). MR0235228 (38 #3539) 6. V. I. Arnol'd, Mathematical Methods of Classical Mechanics [in Russian], Nauka, Moscow (1989). MR1037020 (93c:70001) 7. D. K. Arrowsmith and C. M. Place, Ordinary Differential Equations. Qualitative Theory with Applications [Russian translation], Mir, Moscow (1986). 8. I. Bendixon, "On curves defined by differential equations," Usp. Mat. Nauk, 9 (1941). 9. I. T. Borisenok, B. Ya. Lokshin, and V. A. Privalov, "On flight dynamics of axially symmetric rotating bodies in the air," Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, 2, 3542 (1984). 10. A. D. Bryuno, Local Method of Nonlinear Analysis of Differential Equations [in Russian], Nauka, Moscow (1979). MR0542758 (82b:34033) 11. G. S. Byushgens and R. V. Studnev, Dynamics of Longitudinal and Lateral Motion [in Russian], Mashinostroenie, Moscow (1969). 12. G. S. Byushgens and R. V. Studnev, Aircraft Dynamics. Spatial Motion [in Russian], Mashinostroenie, Moscow (1988). 13. S. A. Chaplygin, Selected Works [in Russian], Nauka, Moscow (1976). MR0424502

(54 #12464) 14. V. A. Eroshin, V. A. Samsonov, and M. V. Shamolin, "A model problem of body drag in a resisting medium," Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, 3, 23 27 (1995). 15. C. Godbillon, Differential Geometry and Analytical Mediantes [Russian translation], Mir, Moscow (1973). 16. V. V. Golubev, Lectures on Analytic Theory of Differential Equations [in Russian], Gostekhizdat, Moscow-Leningrad (1950). MR0014552 (7,301a) 17. V. V. Golubev, Lectures on Integrating Equations of Motion of a Heavy Rigid Body Around a Fixed Point [in Russian], Gostekhizdat, Moscow-Leningrad (1953). 18. M. I. Gurevich, Jet Theory of Ideal Fluids [in Russian], Nauka, Moscow (1979). 19. V. V. Kozlov, "Integrability and non-integrability in Hamiltonian mechanics," Usp. Mat. Nauk, 38, No. 1, 367 (1983). MR0693718 (84k:58076) 20. S. Lcftschetz, Geometric Theory of Differential Equations [Russian translation], IL, Moscow (1961). 21. B. Ya. Lokshin, V. A. Privalov, and V. A. Samsonov, Introduction to the Problem of Body Motion in a Resisting Medium [in Russian], MGU, Moscow (1986). 22. B. Ya. Lokshin, V. A. Privalov, and V. A. Samsonov, Introduction to the Problem on Motion of a Point and a Body in a Resisting Medium [in Russian], MGU, Moscow (1992). 23. B. Ya. Lokshin, Yu. M. Okunev, V. A. Samsonov, and M. V. Shamolin, "Some integrable cases of rigid body spatial oscillations in a resisting medium," In: Abstracts of Reports of the XXIst Scientific Readings in Cosmonautics (Moscow, 2831.01.1997) [in Russian], IIET RAN, Moscow (1997), pp. 8283. 24. Yu. I. Manin, "Algebraic aspects of nonlinear differential equations," In: Progress in Science and Technology, Series on Contemporary Problems in Mathematics [in Russian], Vol. 11, AU-Union Institute for Scientific and Technical Information, USSR Academy of Sciences, Moscow (1978), pp. 5112. MR0501136 (58 #18567) 25. W. Miller, Symmetry and Separation of Variables [Russian translation], Mir, Moscow (1981). MR0645900 (83a:58098) 26. V. V. Nemytskii and V. V. Stepanov, Qualitative Theory of Differential Equations [in Russian], Gostekhizdat, Moscow-Leningrad (1949). 27. Yu. M. Okunev and V. A. Sadovnichii, "Model dynamical systems of a certain problem of exterior ballistics and their analytical solutions," In: Problems of Modern Mechanics [in Russian], MGU, Moscow (1998), pp. 2846. 28. Yu. M. Okunev, V. A. Privalov, and V. A. Samsonov, "Some problems of body motion in a resisting medium," In: Proceedings of the Al l-Union Conference "Nonlinear Phenomena" [in Russian], Nauka, Moscow (1991), pp. 140144. 29. Yu. M. Okunev, V. A. Sadovnichii, V. A. Samsonov, and G. G. Chernyi, "Complex of modelling of flight dynamics problems," Vestn. MGU, Mat., Mekh., No. 6, 6675 (1996). 30. A. Poincarґ On Curves Defined by Differential Equations [Russian translation], e, OGIZ, Moscow-Leningrad (1947). 31. V. A. Samsonov and M. V. Shamolin, On the problem of body motion in a resisting medium," Vestn. MGU, Mat., Mekh., No. 3, 5154 (1989). MR1029730 (90k:70007) 32. M. V. Shamolin, "Classification of phase portraits in the problem of body motion in a resisting medium in the presence of a linear damping moment," Prikl. Mat. Mekh, 57, No. 4, 4049 (1993). MR1258007 (94i:70027) 33. M. V. Shamolin, "Introduction to the problem of body drag in a resisting medium and a new two-parametric family of phase portraits," Vestn. MGU, Mat., Mekh., No. 4, 5769 (1996). MR1644665 (99e:70027)

34. M. V. Shamolin, "Spatial Poincarґ topographical systems and comparison systems," e Usp. Mat. Nauk, 52, No. 3, 177178 (1997). MR1479402 (99a:34089) 35. M. V. Shamolin, "On integrability in transcendental functions," Usp. Mat. Nauk, 53, No. 3, 209210 (1998). MR1657632 (99h:34006) 36. M. V. Shamolin, "On limits sets of differential equations near singular points," Usp. Mat. Nauk, 55, No. 3, 187188 (2000). MR1777365 (2002d:34049) 37. M. V. Shamolin, "Model problem of body motion in a resisting medium taking account of the dependence of the resistance force moment on angular velocity," In: Scientific Report of the Institute of Mechanics, Moscow State University [in Russian], No. 4818, MGU, Moscow (2006), p. 44. 38. M. V. Shamolin, "Integrability of strongly nonconservative systems in transcendental elementary functions," In: Abstracts of Sessions of the Workshop "Topical Problems of Geometry and Mechanics," Contemporary Mathematics, Fundamental Direction [in Russian], 23 (2007). p. 40. 39. M. V. Shamolin, "Complete integrability of equations of spatial pendulum motion in medium flow taking account of rotational derivatives of its action force moment," Izv. Ross. Akad. Nauk, Mech. Tverd. Tela, 3, 187192 (2007). 40. M. V. Shamolin, Methods for Analysis of Dynamical Systems with Variable Dissipation in Rigid Body Dynamics [in Russian], Examen, Moscow (2007). 41. M. V. Shamolin, Some Problems of Differential and Topological Diagnosis [in Russian], 2nd Revised and Supplementary Edition, Examen, Moscow (2007). 42. M. V. Shamolin and D. V. Shebarshov. "Lagrange tori and the the Hamilton-Jacobi equation," In: Book of Abstracts of the Conference PDE Prague'98 (Praha, August 1016, 1998; Partial Differential Equations: Theory and Numerical Solutions); Charles University, Praha, Czech Rep. (1998), p. 88. 43. M. V. Shamolin, "New integrable cases and families of portraits in the plane and spatial dynamics of a rigid body interacting with a medium," J. Math. Sci., 114, No. 1, 919975 (2003). MR1965083 (2004d:70008) 44. G. K. Suslov, Theoretical Mechanics [in Russian], Gostekhizdat, Moscow (1946). 45. Ya. V. Tatarinov, Lectures on Classical Dynamics [in Russian], MGU, Moscow (1984). 46. E. T. Whitaker, Analytical Dynamics [Russian translation], ONTI, Moscow (1937). 47. N. E. Zhukovskii, "On fall of light oblong bodies rotating around their longitudinal axes," In: Complete Col lection of Works [in Russian], Vol. 5. Kizmatgiz. Moscow (1937), pp. 7280, 100 115. 48. N. E. Zhukovskii, "On bird soaring," In: Comple the Col lection of Works [in Russian], Vol. 5, Fizmatgiz, Moscow (1937), pp. 4959.
Note: This list reflects references listed in the original paper as accurately as possible with no attempt to correct errors.

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MR2828395 (2012d:76003) 76A02 A idagulov, R. R. (RS-MOSC-MC) ; Shamolin, M. V. (RS-MOSC-MC) Averaging op erators and real equations of fluid mechanics. (Russian. Russian summary)

Sovrem. Mat. Prilozh. No. 65, Matematicheskaya Fizika, Kombinatorika i Optimal noe Upravlenie (2009), 3146; translation in J. Math. Sci. (N. Y.) 165 (2010), no. 6, 637653. Summary (translated from the Russian): "We discuss pseudodifferential operators that appear in real equations of continuum mechanics."
References

1. R. R. Aidagulov and M. V. Shamolin, "A phenomenological approach to finding interphase forces," Dokl. Ross. Akad. Nauk, 412, No. 1, 4447 (2007). MR2449984 2. R. R. Aidagulov and M. V. Shamolin, "A general spectral approach to continuous medium dynamics," Sovremennaya Matematika. Fundamental'nye Napravleniya, 23, 5270 (2007). MR2342524 (2009g:74015) 3. R. F. Ganiev, L. E. Ukrainskii, and O. R. Ganiev "Resonant filtration flows in a porous medium saturated with a fluid," Dokl. Ross. Akad. Nauk, 412, No. 1 (2007). 4. F. John, Plane Waves and Spherical Means Applied to Partial Differential Equations [Russian translation], IL, Moscow (1958). 5. A. G. Kulikovskii and E. I. Sveshnikova, Nonlinear Waves in Elastic Media [in Russian], Moskovskii Lizei, Moscow (1998). 6. A. A. Lokshin and Yu. V. Suvorova, Mathematical Theory of Wave Propagation in Media With Memory [in Russian], MGU, Moscow (1982). MR0676810 (84m:73031) 7. A. N. Osiptsov, "On accounting for volume finiteness and hydrodynamic interaction of particles in gas suspensions," Dokl. Akad. Nauk SSSR, 275, No. 5, 10731076 (1984). 8. R. Penrose, The Road to Reality: A Complete Guide to the Laws of the Universe [Russian translation], Reg. Khaotic Dinamik, Moscow-Izhevsk (2007). MR2116746 (2005k:83002) 9. V. Ya. Rudyak, Statistical Theory of Dissipative Processes in Gases and Fluids [in Russian], Nauka, Novosibirsk (1987). 10. M. Sato, "Theory of hyperfunctions. I, II," J. Fac. Shi. Univ. Tokyo, Sect. I, 139193 (1959); 387437 (1960). MR0114124 (22 #4951) 11. M. V. Shamolin, Some Problems of Differential and Topological Diagnosis [in Russian], 2nd Revised and Supplemented Edition, Ekzamen, Moscow (2007), pp. 240 281. 12. M. A. Shubin, Pseudodifferential Operators and Spectral Theory [in Russian], Nauka, Moscow (1979). MR0509034 (80h:47057)
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MR2828394 (2012e:35277) 35S05 47G30 76T30 A idagulov, R. R. (RS-MOSC-MC) ; Shamolin, M. V. (RS-MOSC-MC) Pseudo differential op erators in the theory of multiphase multivelo city flows. (Russian. Russian summary)

Sovrem. Mat. Prilozh. No. 65, Matematicheskaya Fizika, Kombinatorika i Optimal noe Upravlenie (2009), 1130; translation in J. Math. Sci. (N. Y.) 165 (2010), no. 6, 616636. The article concerns methodological principles of the theory of mechanical systems. The authors show that the adequate description of multiphase multivelocity flows must use not differential but pseudodifferential equations and these equations must be hyperbolic. Yu. V. Egorov
References

1. R. R. Aidagulov and M. V. Shamolin, "General spectral approach to continuousmedium dynamics," In: Contemporary Mathematics. Fundamental Directions [in Russian], 23, RUDN, Moscow (2007), pp. 5270. MR2342524 (2009g:74015) 2. R. R. Aidagulov and M. V. Shamolin, "A phenomenological approach to finding interphase forces," Dokl. Ross. Akad. Nauk, 412, No. 1, 4447 (2007). MR2449984 3. Yu. V. Egorov and M. A. Shibin, "Linear partial differential equations. Elements of modern theory," In: Progress in Science and Technology, Series on Contemporary Problems in Mathematics, Fundamental Directions [in Russian], Vol. 31, All-Union Institute of Scientific and Technical Information, USSR Academy of Sciences, Moscow (1988), pp. 5125. 4. I. M. Gel'fand and G. E. Shilov, Generalized Functions [in Russian], Fizmatgiz, Moscow (1958). 5. E. Hewitt and K. Ross, Abstract Harmonic Analysis [Russian translation], Vol. 2, Mir, Moscow (1975). MR0396828 (53 #688) 6. F. John, Plane Waves and Spherical Means as Applied to Partial Differential Equations [Russian translation], IL, Moscow (1958). 7. A. G. Kulikovskii and E. I. Sveshnikova, Nonlinear Waves in Elastic Media [in Russian], Moskovskii Litsei, Moscow (1998). 8. A. G. Kulikovskii and N. T. Pashchenko, "Structure of the relaxation zone of the light absorption wave and regimes of self-supporting light denotation waves," In: Scientific Report of the Institute of Mechanics, Moscow State University [in Russian], No. 4623, Institute of Mechanics, Moscow State University, Moscow (2002). 9. V. P. Maslov, Operator Methods [in Russian], Nauka, Moscow (1973). MR0445305 (56 #3647) 10. S. Mizohata, Theory of Partial Differential Equations [Russian translation], Mir, Moscow (1977). 11. R. I. Nigmatullin, Foundation of Heterogeneous-Medium Mechanics [in Russian], Nauka, Moscow (1978). 12. V. N. Nikolaevskii, Geomechanics and Fluid Dynamics [in Russian], Nedra, Moscow (1996). 13. A. N. Osiptsev, "On accounting for the volume finiteness and particle hydrodynamic interaction in gas mixtures," Dokl. Akad. Nauk SSSR, 275, No. 5, 10731076 (1984). 14. R. Penrose, The Road to Reality: A Complete Guide to the Laws of the Universe [Russian translation], Regional'naya i Khaoticheskaya Dinamika, Moscow-Izhevsk (2007). MR2116746 (2005k:83002) 15. M. Sato, "Theory of hyperfunctions. I," J. Fac. Shi. Univ. Tokyo. Sect. I, 8, 139193 (1959). MR0114124 (22 #4951)

16. M. Sato, "Theory of hyperfunctions. II," J. Fac. Shi. Univ. Tokyo. Sect. I, 8, 387437 (1960). MR0132392 (24 #A2237) 17. M. V. Shamolin, Some Problems of Differential and Topological Diagnosis [in Russian], 2nd Revised and Supplemented Edition, Ekzamen, Moscow (2007).
Note: This list reflects references listed in the original paper as accurately as possible with no attempt to correct errors.

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MR2676332 (2011g:37069) 37C99 34C14 34M35 37E99 70E15 Shamolin, M. V. (RS-MOSC-IMC) On the integrability in elementary functions of some classes of nonconservative dynamical systems. (Russian. Russian summary)

Sovrem. Mat. Prilozh. No. 62, Geometriya i Mekhanika (2009), 130170; translation in J. Math. Sci. (N. Y.) 161 (2009), no. 5, 734778. Summary (translated from the Russian): "The results in this paper are based on the investigation of the applied problem of the motion of a rigid body in a resisting medium [V. A. Samsonov, B. Ya. Lokshin and V. A. Privalov, "Qualitative analysis" (Russian), Sci. Rep. Inst. Mech. Moscow State Univ. No. 3425, Moskov. Gos. Univ., Moscow, 1985; per bibl.; V. A. Samsonov et al., "Mathematical modeling in the problem of the deceleration of a body in a resisting medium in the case of a jet flow around the body" (Russian), Sci. Rep. Inst. Mech. Moscow State Univ. No. 4396, Moskov. Gos. Univ., Moscow, 1995; per bibl.], in which complete lists of transcendental first integrals expressed in terms of a finite combination of elementary functions were obtained. This made it possible to thoroughly analyze all the phase tra jectories and to determine which of their properties possess structural stability and which are preserved in systems of more general form. The complete integrability of such systems is related to hidden symmetries. Therefore, it is of interest to study sufficiently wide classes of dynamical systems that have similar hidden symmetries. "As is known, the concept of integrability is, in general, fairly broad. Thus, it is necessary to take into account in what sense it is understood (a criterion according to which one can conclude that the structure of the tra jectories of the dynamical system considered is especially `attractive and simple') in the function classes in which the first integrals are sought, etc. "In this paper, we use an approach in which the first integrals are transcendental functions, and in fact elementary. Here transcendence is understood not in the sense of elementary functions (for example, trigonometric) but in the sense that they have essentially singular points (according to the classification used in the theory of functions of one complex variable in the case when the function has essentially singular points). In this connection, it is necessary to continue them formally to the complex plane. As a rule, such systems are strongly nonconservative."
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around," In: Scientific Report of Institute of Mechanics, Moscow State University [in Russian], No. 4396, Moscow (1995). G. Sansone, Ordinary Differential Equations [Russian translation], IL, Moscow (1954). L. I. Sedov, Continuous Medium Mechanics [in Russian], Vols. 1, 2, Nauka, Moscow (19831984). H. Seifert and W. Threifall, Topology [Russian translation], Gostekhizdat, MoscowLeningrad (1938). N. Yu. Seiivanova and M. V. Shamolin, "Extended Cahn-Hillard model and certain its solutions," In: Materials of Voronezh Al l-Russion Conference `Pontryagin Readings-XVIII,' Voronezh, May, 2007 [in Russian], Voronezh State University, Voronezh (2007), pp. 145146. M. V. Shamolin, Qualitative Analysis of a Model Problem of Body Motion in a Medium with Streamline Flow Around [in Russian], Candidate Dissertation, MGU, Moscow (1991). M. V. Shamolin, "Closed tra jectories of different topological type in problem of body motion in a medium with resistance," Vestn. MGU, Ser. 1, Mat., Mekh., 2, 5256 (1992). MR1293705 (95d:34060) M. V. Shamolin, "To problem of body motion in a medium with resistance," Vestn. MGU, Ser. 1, Mat., Mekh., 1, 5258 (1992). MR1214592 (93k:70028) M. V. Shamolin, "Classification of phase portraits in problem of body motion in a resisting medium under presence of a linear damping moment," Prikl. Mat. Mekh., 57, No. 4, 4049 (1993). MR1258007 (94i:70027) M. V. Shamolin, "A new two-parameter family of phase portraits for problem of a body motion in a resisting medium," In: Model ling and Study of Stability of Systems, Scientific Conference, May 2428, 1993. Abstracts of Reports, Pt. 2 [in Russian], Znanie, Kiev (1993), pp. 6263. M. V. Shamolin, "Relative structural stability of problem of body motion in a resisting medium," In: Mechanics and Its Applications, Scientific Conference, November 911, 1993, Abstracts of Reports, Tashkent State University, Tashkent (1993), pp. 2021. M. V. Shamolin, "Applications of Poincarґ topographical system methods and e comparison systems in some concrete systems of differential equations," Vestn. MGU, Ser. 1, Mat., Mekh., 2, 6670 (1993). MR1223987 (94b:34060) M. V. Shamolin, "Existence and uniqueness of tra jectories having infinitely distant points as limit sets for dynamical systems on plane," Vestn. MGU, Ser. 1, Mat., Mekh., 1, 6871 (1993). MR1293942 (95e:34036) M. V. Shamolin, "A new two-parameter family of phase portraits in problem of a body motion in a medium," Dokl. Ross. Akad. Nauk, 337, No. 5, 611614 (1994). MR1298329 (95g:70006) M. V. Shamolin, "On relative roughness of dynamical systems in problem of body motion in a medium under streamline flow around," In: Model ling and Study of Stability of Systems, Scientific Conference, May 1620, 1994, Abstract of Reports [in Russian], Kiev (1994), pp. 144145. M. V. Shamolin, "A new two-parameter family of phase portraits with limit cycles in rigid body dynamics interacting with a medium," In: Model ling and Study of Stability of Systems, Scientific Conference, May 1519, 1995, Abstracts of Reports (Study of Systems) [in Russian], Kiev (1995), p. 125. M. V. Shamolin, "Relative structural stability of dynamical systems for problem of body motion in a medium," In: Analytical, Numerical, and Experimental Methods in Mechanics. A Col lection of Scientific Works [in Russian], MGU, Moscow (1995),

pp. 1419. MR1809236 228. M. V. Shamolin, "On relative roughness of dynamical systems in problem of body motion in a resisting medium," In: Abstracts of Reports of Chebyshev Readings, Vestn. VGU, Ser. 1, Mat., Mekh., 6, 17 (1995). 229. M. V. Shamolin, "Definition of relative roughness and two-parameter family of phase portraits in rigid body dynamics," Usp. Mat. Nauk, 51, No. 1, 175176 (1996). MR1392692 (97f:70010) 230. M. V. Shamolin, "Periodic and Poisson stable tra jectories in problem of body motion in a resisting medium," Izv. Ross. Akad. Nauk, Mekhanika Tverdogo Tela, 2, 5563 (1996). 231. M. V. Shamolin, "Spatial Poincarґ topographical systems and comparison systems," e In: Abstracts of Reports of Mathematical Conference `Erugin Readings,' Brest, May 1416, 1996 [in Russian], Brest (1996), p. 107. MR1479402 (99a:34089) 232. M. V. Shamolin, "Introduction to spatial dynamics of rigid body motion in resisting medium." In: Materials of International Conference and Chebyshev Readings Devoted to the 175th Anniversary of P. L. Chebyshev, Moscow, May 1419, 1996, Vol. 2 [in Russian], MGU, Moscow (1996), pp. 371373. 233. M. V. Shamolin, "A list of integrals of dynamical equations in spatial problem of body motion in a resisting medium," In: Model ling and Study of Stability of Systems, Scientific Conference, May 2024, 1996. Abstracts of Reports (Study of Systems), [in Russian], Kiev (1996), p. 142. 234. M. V. Shamolin, "Variety of types of phase portraits in dynamics of a rigid body interacting with a resisting medium," Dokl. Ross. Akad. Nauk, 349, No. 2, 193197 (1996). MR1440994 (98b:70009) 235. M. V. Shamolin, "Qualitative methods in dynamics of a rigid body interacting with a medium," In: II Siberian Congress in Applied and Industrial Mathematics, Novosibirsk, June 2530, 1996. Abstracts of Reports. Pt. III [in Russian], Novosibirsk (1996), p. 267. 236. M. V. Shamolin, "On a certain integrable case in dynamics of spatial body motion in a resisting medium," In: II Symposium in Classical and Celestial Mechanics. Abstracts of Reports, Velikie Luki, August 2328, 1996 [in Russian], Moscow-Velikie Luki (1996), pp. 9192. 237. M. V. Shamolin, "Introduction to problem of body drag in a resisting medium and a new two-parameter family of phase portraits," Vestn. MGU, Ser. 1, Mat., Mekh., 4, 5769 (1996). MR1644665 (99e:70027) 238. M. V. Shamolin, "On an integrable case in spatial dynamics of a rigid body interacting with a medium," Izv. Ross. Akad. Nauk, Mekhanika Tverdogo Tela, 2, 6568 (1997). 239. M. V. Shamolin, "Jacobi integrability of problem of a spatial pendulum placed in over-running medium flow," In: Model ling and Study of Systems. Scientific Conference, May, 1923, 1997. Abstracts of Reports [in Russian], Kiev (1997), p. 143. 240. M. V. Shamolin, "Partial stabilization of body rotational motions in a medium under a free drag," In: Abstracts of Reports of Al l-Russian Conference with International Participation `Problems of Celestial Mechanics,' St. Petersburg, June 36, 1997, Institute of Theoretical Astronomy [in Russian], Institute of theoretical Astronomy, Russian Academy of Sciences, St. Petersburg (1997), pp. 183184. 241. M. V. Shamolin, "Spatial Poincarґ topographical systems and comparison systems," e Usp. Mat. Nauk, 52, No. 3, 177178 (1997). MR1479402 (99a:34089) 242. M. V. Shamolin, "Mathematical modelling of dynamics of a spatial pendulum flowing around by a medium," In: Proceedings of VII International Symposium `Methods of Discrete Singularities in Problems of Mathematical Physics', June 26

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29, 1997, Feodociya [in Russian], Kherson State Technical University, Kherson (1997), pp. 153154. M. V. Shamolin, "Spatial dynamics of a rigid body interacting with a medium," In: Workshop in Mechanics of Systems and Problems of Motion Control and Navigation, Izv. Ross. Akad. Nauk, Mekhanika Tverdogo Tela, 4, 174 (1997). M. V. Shamolin, "Qualitative methods in dynamics of a rigid body interacting with a medium," In: YSTM'96: `Young People and Science, the Third Mil lenium,' Proceedings of International Conference (Ser. Professional) [in Russian], Vol. 2, NTA "APFN," Moscow (1997), pp. I-4. M. V. Shamolin, "Qualitative and numerical methods in some problems of spatial dynamics of a rigid body interacting with a medium," In: Abstracts of Reports of 5th International ConferenceWorkshop `Engineering-Physical Problems of New Technics,' Moscow, May 1922, 1998 [in Russian], Moscow State Technical University, Moscow (1998), pp. 154155. M. V. Shamolin, "Some problems of spatial dynamics of a rigid body interacting with a medium under quasi-stationarity conditions," In: Abstracts of Reports of Al lRussian Scientific-Technical Conference of Young Scientists `Modern Problems of Aero-Cosmous Science,' Zhukovskii, May 2729, 1998 [in Russian], Central AeroHydrodynamical Institute, Moscow (1998), pp. 8990. M. V. Shamolin, "Absolute and relative structural stability in spatial dynamics of a rigid body interacting with a medium," In: Proceedings of International Conference `Mathematics in Industry', ICIM-98, Taganrog, June 29- July 03, 1998 [in Russian], Taganrog State Pedagogical Institute, Taganrog (1998), pp. 332333. M. V. Shamolin, "On integrability in transcendental functions," Usp. Mat. Nauk, 53, No. 3, 209210 (1998). MR1657632 (99h:34006) M. V. Shamolin, "Families of three-dimensional phase portraits in spatial dynamics of a rigid body interacting with a medium," In: III International Symposium in Classical and Celestial Mechanics, August 2327, 1998, Velikie Luki. Abstracts of Reports [in Russian], Computational Center of Russian Academy of Sciences, Moscow-Velikie Luki (1998), pp. 165167. M. V. Shamolin, "Methods of nonlinear analysis in dynamics of a rigid body interacting with a medium," In: CD-Proceedings of the Congress `Nonlinear Analysis and Its Applications', Moscow, Russia, Sept. 15, 1998 [in Russian], Moscow (1999), pp. 497508. M. V. Shamolin, "Family of portraits with limit cycles in plane dynamics of a rigid body interacting with a medium," Izv. Ross. Akad. Nauk, Mekhanika Tverdogo Tela, 6, 2937 (1998). M. V. Shamolin, "Certain classes of partial solutions in dynamics of a rigid body interacting with a medium," Izv. Ross. Akad. Nauk, Mekhanika Tverdogo Tela, 2, 178189 (1999). M. V. Shamolin, "New Jacobi integrable cases in dynamics of a rigid body interacting with a medium," Dokl. Ross. Akad. Nauk, 364, No. 5, 627629 (1999). MR1702618 (2000k:70008) M. V. Shamolin, "On roughness of dissipative systems and relative roughness and non-roughness of variable dissipation systems," Usp. Mat. Nauk, 54, No. 5, 181182 (1999). MR1741681 (2000j:37021) M. V. Shamolin, "A new family of phase portraits in spatial dynamics of a rigid body interacting with a medium," Dokl. Ross. Akad. Nauk, 371, No. 4, 480483 (2000). MR1776307 (2001k:70006) M. V. Shamolin, "On roughness of disspative systems and relative roughness of variable dissipation systems," In: Abstracts of Reports of Workshop in Vector and

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Tensor Analysis Named after P. K. Rashevskii, Vestn. MGU, Ser. 1, Mat., Mekh., 2, 63 (2000). M. V. Shamolin, "On limit sets of differential equations near singular points," Usp. Mat. Nauk, 55, No. 3, 187188 (2000). MR1777365 (2002d:34049) M. V. Shamolin, "Jacobi integrability in problem of four-dimensional rigid body motion in a resisting medium," Dokl. Ross. Akad. Nauk, 375, No. 3, 343346. (2000). MR1833828 (2002c:70005) M. V. Shamolin, "On stability of motion of a body twisted around its longitudinal axis in a resisting medium," Izv. Ross. Akad. Nauk, Mekhanika Tverdogo Tela 1, 189193 (2001). M. V. Shamolin, "Complete integrability of equations for motion of a spatial pendulum in overrunning medium flow," Vestn. MGU, Ser. 1, Mat., Mekh., 5, 2228 (2001). MR1868040 (2002f:70005) M. V. Shamolin, "Problem of four-dimensional body motion in a resisting medium and a certain case of integrability," In: Book of Abstracts of the Third International Conference "Differential Equations and Applications," St. Petersburg, Russia, June 1217, 2000 [in Russian], St. Petersburg State University, St. Petersburg (2000), p. 198. M. V. Shamolin, "On limit sets of differential equations near singular points,", Usp. Mat. Nauk, 55, No. 3, 187188 (2000). MR1777365 (2002d:34049) M. V. Shamolin, "Many-dimensional topographical Poincarґ systems and transcene dental integrability," In: IV Siberian Congress in Applied and Industrial Mathematics, Novosibirsk, June 26-July 01, 2000. Abstracts of Reports, Pt. I. [in Russian], Novosibirsk, Institute of Mathematics (2000), pp. 2526. M. V. Shamolin, "Jacobi integrability of problem of four-dimensional body motion in a resisting medium," In: Abstracts of Reports of International Conference in Differential Equations and Dynamical Systems, Suzdal', August 2126, 2000 [in Russian], Vladimir, Vladimir State University (2000), pp. 196197. M. V. Shamolin, "Comparison of certain integrability cases from two-, three-, and four-dimensional dynamics of a rigid body interacting with a medium," In: Abstracts of Reports of V Crimeanian International Mathematical School `Lyapunov Function Method and Its Application,' (LFM-2000), Crimea, Alushta, September 513, 2000 [in Russian], Simpheropol' (2000), p. 169. M. V. Shamolin, "On a certain case of Jacobi integrability in dynamics of a fourdimensional rigid body interacting with a medium," In: Abstracts of Reports of International Conference in Differential and Integral Equations, Odessa, September 1214, 2000 [in Russian], AstroPrint, Odessa (2000), pp. 294295. M. V. Shamolin, "On stability of motion of a rigid body twisted around its longitudinal axis in a resisting medium," Izv. Ross. Akad. Nauk, Mekhanika Tverdogo Tela, 1, 189193 (2001). M. V. Shamolin, "Variety of types of phase portraits in dynamics of a rigid body interacting with a medium," In: Abstracts of Sessions of Workshop `Actual Problems of Geometry and Mechanics,' Fund. Prikl. Mat., 7, No. 1, 302303 (2001). M. V. Shamolin, "Integrability of a problem of four-dimensional rigid body in a resisting medium," In: Abstracts of Sessions of Workshop `Actual Problems of Geometry and Mechanics,' Fund. Prikl. Mat., 7, No. 1, 309 (2001). M. V. Shamolin, "New integrable cases in dynamics of a four-dimensional rigid body interacting with a medium," In: Abstracts of Reports of Scientific Conference, May 2225, 2001 [in Russian], Kiev (2001), p. 344. M. V. Shamolin, "Integrability cases of equations for spatial dynamics of a rigid body," Prikl. Mekh., 37, No. 6, 7482 (2001). MR1872149 (2002i:70006)

272. M. V. Shamolin, "New Jacobi integrable cases in dynamics of two-, three-, and fourdimensional rigid body interacting with a medium," In: Absracts of Reports of VIII Al l-Russian Congress in Theoretical and Applied Mechanics, Perm', August 2329, 2001 [in Russian], Ural Department of Russian Academy of Sciencesm Ekaterinburg (2001), pp. 599600. 273. M. V. Shamolin, "On integrability of certain classes of nonconservative systems," Usp. Mat. Nauk, 57, No. 1, 169170 (2002). MR1914556 (2003g:34019) 274. M. V. Shamolin, "New integrable cases in dynamics of a two-, three-, and fourdimensional rigid body interacting with a medium," In: Abstracts of Reports of International Conference in Differential Equations and Dynamical Systems, Suzdal', July 16, 2002 [in Russian], Vladimir State University, Vladimir (2002), pp. 142 144. 275. M. V. Shamolin, "On a certain spatial problem of rigid body motion in a resisting medium," In: Abstracts of Reports of International Scientific Conference `Third Polyakhov Readings,' St. Petersburg, February 46, 2003 [in Russian], NIIKh St. Petersburg Univ, (2003), pp. 170171. 276. M. V. Shamolin, "Integrability in transcendental functions in rigid body dynamics," In: Abstracts of Reports of Scientific Conference `Lomonosov Readings,' Sec. Mechanics, April 1727, 2003, Moscow, M. V. Lomonosov Moscow State University [in Russian], MGU, Moscow (2003), p. 130. 277. M. V. Shamolin, "On integrability of nonconservative dynamical systems in transcendental functions," In: Model ling and Study of Stability of Systems, Scientific Conference, May 2730, 2003, Abstracts of Reports [in Russian], Kiev (2003), p. 277. 278. M. V. Shamolin, "Geometric representation of motion in a certain problem of body interaction with a medium," Prikl. Mekh., 40, No. 4, 137144 (2004). MR2131714 (2005m:70050) 279. M. V. Shamolin, "Integrability of nonconservative systems in elementary functions," In: X Mathematical International Conference Named after Academician M. Kravchuk, September 315, 2004, Kiev [in Russian], Kiev (2004), p. 279. 280. M. V. Shamolin, Methods for Analysis of Classes of Nonconservative Systems in Dynamics of a Rigid Body Interacting with a Medium [in Russian], Doctorial Dissertation, MGU, Moscow (2004), p. 329. 281. M. V. Shamolin, Some Problems of Differential and Topological Diagnostics [in Russian], Ekzamen, Moscow (2004). 282. M. V. Shamolin, "On rigid body motion in a resisting medium taking account of rotational derivatives of areodynamic force moment in angular velocity," In: Modelling and Studying of Systems, Scientific Conference, May 2325, 2005. Abstracts of Reports [in Russian], Kiev (2005), p. 351. 283. M. V. Shamolin, "Cases of complete integrability in dynamics of a four-dimensional rigid body interacting with a medium," In: Abstracts of Reports of International Conference `Functional Spaces, Approximation Theory, and Nonlinear Analysis' Devoted to the 100th Anniversary of A. M. Nikol'skii, Moscow, May 2329, 2005 [in Russian], V. A. Steklov Mathematical Institute of Russian Academy of Sciences, Moscow (2005), p. 244. 284. M. V. Shamolin, "On a certain integrable case in dynamics on so(4) в R4 ," In: Abstracts of Reports of Al l-Russian Conference `Differential Equations and Their Applications,' (SamDif-2005), Samara, June 27-Jily 2, 2005 [in Russian], UniversGrupp, Samara (2005), pp. 9798. 285. M. V. Shamolin, "A case of complete integrability in spatial dynamics of a rigid body interacting with a medium taking account of rotational derivatives of force

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moment in angular velocity," Dokl. Ross. Akad. Nauk, 403, No. 4, 482485 (2005). MR2216035 (2006m:70012) M. V. Shamolin, "Comparison of Jacobi integrable cases of plane and spatial body motions in a medium under streamline flow around," Prikl. Mat. Mekh., 69, No. 6, 10031010 (2005). MR2252203 (2007c:70009) M. V. Shamolin, "On body motion in a resisting medium taking account of rotational derivatives of aerodynamic force moment in angular velocity," In: Abstracts of Reports of Scientific Conference `Lomonosov Readings-2005,' Sec. Mechanics, April, 2005, Moscow, M. V. Lomonosov Moscow State University [in Russian], MGU, Moscow (2005), p. 182. M. V. Shamolin, "Variable dissipation dynamical systems in dynamics of a rigid body interacting with a medium," In: Differential Equations and Computer Algebra Tools, Materials of International Conference, Brest, October 58, 2005, Pt. 1. [in Russian], BGPU, Minsk (2005), pp. 231233. M. V. Shamolin, "On a certain integrable case of equations of dynamics in so(4) в Rn ," Usp. Mat. Nauk, 60, No. 6, 233234 (2005). MR2225204 (2007a:70009) M. V. Shamolin, "Integrability in transcendental functions in rigid body dynamics," In: Mathematical Conference `Modern Problems of Applied Mathematics and Mathematical Model ling, Voronezh, December 1217, 2005 [in Russian], Voronezh State Academy, Voronezh (2005), p. 240. M. V. Shamolin, "Variable dissipation systems in dynamics of a rigid body interacting with a medium," In: Fourth Polyakhov Readings, Abstracts of Reports of International Scientific Conference on Mechanics, St. Petersburg, February 710, 2006 [in Russian], VVM, St. Petersburg (2006), p. 86. M. V. Shamolin, "Model problem of body motion in a resisting medium taking account of dependence of resistance force on angular velocity," In: Scientifuc Report of Institute of Mechanics, Moscow State University [in Russian], No. 4818, Institute of Mechanics, Moscow State University, Moscow (2006), p. 44. M. V. Shamolin, "To problem on rigid body spatial drag in a resisting medium," Izv. Ross. Akad. Nauk, Mekhanika Tverdogo Tela, 3, 4557 (2006). M. V. Shamolin, "On tra jectories of characteristic points of a rigid body moving in a medium," In: International Conference `Fifth Okunev Readings,' St. Petersburg, June 2630, 2006. Absracts of Reports [in Russian], Baltic State Technical University, St. Petersburg (2006), p. 34. M. V. Shamolin, "On a case of complete integrability in four-dimensional rigid body dynamics," In: Abstracts of Reports of International Conference in Differential Equations and Dynamical Systems, Vladimir, July 1015, 2006 [in Russian], Vladimir State University, Vladimir (2006), pp. 226228. M. V. Shamolin, "To spatial problem of rigid body interaction with a resisting medium," In: Absracts of Reports of IX Al l-Russian Congress in Theoretical and Applied Mechanics, Nizhnii Novgorod, August 2228, 2006. Vol. I [in Russian], N. I. Lobachevskii Nizhnii Novgorod State Univesity, Nizhnii Novgorod (2006), p. 120. M. V. Shamolin, "Spatial problem on rigid body motion in a resisting medium," In: VIII Crimeanian International Mathematical School `Lyapunov Function Method and Its Applications,' Abstracts of Reports, Alushta, September 1017, 2006, Tavriya National University [in Russian], DiAiPi, Simpheropol' (2006), p. 184. M. V. Shamolin, "Variety of types of phase portraits in dynamics of a rigid body interacting with a medium," In: Abstracts of Sessions of Workshop `Actual Problems of Geometry and Mechanics,' Contemporary Mathematics, Fundamental Directions [in Russian], Vol. 23 (2007), p. 17. M. V. Shamolin, "Integrability of problem of four-dimensional rigid body motion

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in a resisting medium," In: Abstracts of Sessions of Workshop `Actual Problems of Geometry and Mechanics,' Contemporary Mathematics, Fundamental Directions [in Russian], Vol. 23 (2007), p. 21. M. V. Shamolin, "On account of rotational deivatives of a aerodynamic force moment on body motion in a resisting medium," In: Abstracts of Sessions of Workshop `Actual Problems of Geometry and Mechanics,' Contemporary Mathematics, Fundamental Directions [in Russian], Vol. 23 (2007), p. 26. M. V. Shamolin, "New integrable cases in dynamics of a four-dimensional rigid body interacting with a medium," In: Abstracts of Sessions of Workshop `Actual Problems of Geometry and Mechanics,' Contemporary Mathematics, Fundamental Directions [in Russian], Vol. 23 (2007), p. 27. M. V. Shamolin, "On integrability in transcendental functions," In: Abstracts of Sessions of Workshop `Actual Problems of Geometry and Mechanics,' Contemporary Mathematics, Fundamental Directions [in Russian], Vol. 23 (2007), p. 34. M. V. Shamolin, "On integrability of motion of four-dimensional body-pendulum situated in over-running medium flow," In: Abstracts of Sessions of Workshop `Actual Problems of Geometry and Mechanics,' Contemporary Mathematics, Fundamental Directions [in Russian] Vol. 23, (2007), p. 37. M. V. Shamolin, "Integrability in elementary functions of variable dissipation systems," In: Abstracts of Sessions of Workshop `Actual Problems of Geometry and Mechanics,' Contemporary Mathematics, Fundamental Directions [in Russian], Vol. 23 (2007), p. 38. M. V. Shamolin, "Integrability in transcendental elementary functions," In: Abstracts of Sessions of Workshop `Actual Problems of Geometry and Mechanics,' Contemporary Mathematics, Fundamental Directions [in Russian], Vol. 23 (2007), p. 40. M. V. Shamolin, "On rigid body motion in a resisting medium taking account of rotational derivatives of aerodynamic force moment in angular velocity," In: Abstracts of Sessions of Workshop `Actual Problems of Geometry and Mechanics,' Contemporary Mathematics, Fundamental Directions [in Russian], Vol. 23 (2007), p. 44. M. V. Shamolin, "Influence of rotational derivatives of medium interaction force moment in angular velocity of a rigid body on its motion," In: Abstracts of Sessions of Workshop `Actual Problems of Geometry and Mechanics,' Contemporary Mathematics, Fundamental Directions [in Russian], Vol. 23 (2007), p. 44. M. V. Shamolin, "On work of All-Russian Conference `Differential equations and Their Applications,' Samara, June 27-July 29, 2005," In: Abstracts of Sessions of Workshop `Actual Problems of Geometry and Mechanics,' Contemporary Mathematics, Fundamental Directions [in Russian], Vol. 23 (2007), p. 45. M. V. Shamolin, "On integrability in elementary functions of certain classes of nonconservative dynamical systems," In: Model ling and Study of Stability of Systems, Scientific Conference, May 2225, 2007. Abstracts of Reports [in Russian], Kiev (2007), p. 249. M. V. Shamolin, "Case of complete integrability in dynamics of a four-dimensional rigid body in nonconcervative force field," In: `Nonlinear Dynamical Analysis-2007,' Abstracts of Reports of International Congress, St. Petersburg, June 48, 2007 [in Russian], St. Petersburg State University, St. Petersburg (2007), p. 178. M. V. Shamolin, "Cases of complete integrability in elementary functions of certain classes of nonconservative dynamical systems," In: Abstracts of Reports of International Conference `Classical Problems of Rigid Body Dynamics,' June 913, 2007 [in Russian], Institute of Applied Mathematics and Mechanics, National Academy of

Sciences of Ukraine, Donetsk (2007), pp. 8182. 312. M. V. Shamolin, "Complete integrability of equations of motion for a spatial pendulum in medium flow taking account of rotational derivatives of moment of its action force," Izv. Ross Akad. Nauk, Mekhanika Tverdogo Tela, 3, 187192 (2007). 313. M. V. Shamolin, "Cases of complete integrability in dynamics of a four-dimensional rigid body in a nonconservative force field," In: Abstracts of Reports of International Conference `Analysis and Singularities,' Devoted to 70th Anniversary of V. I. Arnol'd, August 2024, 2007, Moscow [in Russian], MIAN, Moscow (2007), pp. 110112. 314. M. V. Shamolin, "A case of complete integrability in dynamics on a tangent bundle of two-dimensional sphere," Usp. Mat. Nauk, 62, No. 5, 169170 (2007). MR2373767 (2008i:37121) 315. M. V. Shamolin, "Cases of complete integrability in dynamics of a rigid body interacting with a medium," In: Abstracts of Reports of Al l-Russiann Conference `Modern Problems of Continuous Medium Mechanics' Devoted to Memory of L. I. Sedov in Connection with His 100th Anniversary, Moscow, November, 1214, 2007 [in Russian], MIAN, Moscow (2007), pp. 166167. 316. M. V. Shamolin, "On stability of a certain regime of rigid body motion in a resisting medium," In: Abstracts of Reports of Scientific Conference `Lomonosov Readings2007,' Sec. Mechanics, Moscow, Moscow State University, April, 2007 [in Russian], MGU, Moscow (2007), p. 153. 317. M. V. Shamolin, Methods for Analysis of Variable Dissipation Dynamical Systems in Rigid Body Dynamics [in Russian], Ekzamen, Moscow (2007). 318. M. V. Shamolin, Some Problems of Differential and Topological Diagnostics [in Russian], 2nd Corrected and Added Edition, Eksamen, Moscow (2007). 319. M. V. Shamolin, "Three-parameter family of phase portraits in dynamics of a rigid body interacting with a medium," Dokl. Ross. Akad. Nauk, 418, No. 1. 4651 (2008). MR2459491 320. M. V. Shamolin and S. V. Tsyptsyn, "Analytical and numerical study of tra jectories of body motion in a resisting medium," In: Scientific Report of Institute of Mechanics, Moscow State University [in Russian], No. 4289, Institute of Mechanics, Moscow State University, Moscow (1993). 321. M. V. Shamolin and D. V. Shebarshov, "Pro jections of Lagrangian tori of a biharmonic oscillator on position space and dynamics of a rigid body interacting with a medium," In: Model ling and Study of Stability of Systems, Scientific Conference May 1923, 1997. Abstracts of Reports [in Russian], Kiev (1997), p. 142. 322. M. V. Shamolin, "Structural stable vector fields in rigid body dynamics, In: Proc. of 8th Conf. on Dynamical Systems (Theory and Applications) (DSTA 2005), Lodz, Poland, Dec. 1215, 2005; Tech. Univ. Lodz., 1, 429436 (2005). 323. M. V. Shamolin, "Global qualitative analysis of the nonlinear systems on the problem of a body motion in a resisting medium," In: Fourth Col loquium on the Qualitative Theory of Differential Equations, Bolyai Institute, August 1821, 1993, Szeged, Hungary (1993), p. 54. 324. M. V. Shamolin, "Relative structural stability on the problem of a body motion in a resisting medium," In: ICM'94, Abstract of Short Communications, Zurich, 311 August, 1994, Zurich, Switzerland (1994), p. 207. 325. M. V. Shamolin, "Structural optimization of the controlled rigid motion in a resisting medium," In: WCSMO-1, Extended Abstracts. Posters, Goslar, May 28-June 2, 1995, Goslar, Germany (1995), pp. 1819. MR1809236 326. M. V. Shamolin, "Qualitative methods to the dynamic model of an interaction of a rigid body with a resisting medium and new two-parametric families of the phase

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portraits," In: DynDays '95 (Sixteenth Annual Informal Workshop), Program and Abstracts, Lyon, June 28-July 1, 1995, Lyon, France (1995), p. 185. M. V. Shamolin, "New two-parameter families of the phase patterns on the problem of a body motion in a resisting medium," In: ICIAM'95, Book of Abstracts, Hamburg, 37 July, 1995, Hamburg, Germany (1995), p. 436. M. V. Shamolin, "Poisson-stable and dense orbits in rigid body dynamics," In: 3rd Experimental Chaos Conference, Advance Program, Edinburg, Scotland, August 2123, 1995, Edinburg, Scotland (1995), p. 114. M. V. Shamolin, "Qualitative methods in interacting with the medium rigid body dynamics," In: Abstracts of GAMM Wissenschaftliche Jahrestangung'96, 2731 May, 1996, Prague, Czech Rep, Karls-Universitat Prag., Prague, (1996), pp. 129 130. M. V. Shamolin, "Relative structural stability and relative structural instability of different degrees in topological dynamics," In: Abstracts of International Topological Conference Dedicated to P. S. Alexandroff 's 100th Birthday `Topology and Applications,' Moscow, May 2731, 1996 [in Russian], Phasys, Moscow (1996), pp. 207208. M. V. Shamolin, "Topographical Poincare systems in many dimensional spaces," In: Fifth Col loquium on the Qualitative Theory of Differential Equations, Bolyai Institute, Regional Committee of the Hungarian Academy of Sciences, July 29August 2, 1996, Szeged, Hungary (1996), p. 45. M. V. Shamolin, "Qualitative methods in interacting with the medium rigid body dynamics," In: Abstracts of XIXth ICTAM, Kyoto, Japan, August 2531, 1996, Kyoto, Japan (1996), p. 285. M. V. Shamolin, "Three-dimensional structural optimization of controlled rigid motion in a resisting medium," In: Proceedings of WCSMO-2, Zakopane, Poland, May 2630, 1997, Zakopane, Poland (1997), pp. 387392. M. V. Shamolin, "Classical problem of a three-dimensional motion of a pendulum in a jet flow," In: 3rd EUROMECH Solid Mechanics Conference, Book of Abstracts, Stockholm, Sweden, August 1822, 1997, Royal Inst. of Technology, Stockholm, Sweden (1997), p. 204. M. V. Shamolin, "Families of three-dimensional phase portraits in dynamics of a rigid body," In: EQUADIFF 9, Abstracts, Enlarged Abstracts, Brno, Czech Rep., August 2529, 1997, Masaryk Univ., Brno, Czech Rep. (1997), p. 76. M. V. Shamolin, "Many-dimensional topographical Poincare systems in rigid body dynamics," In: Abstracts of GAMM Wissenschaftliche Jahrestangung'98, 69 April, 1998, Bremen, Germany, Universitat Bremen, Bremen (1998), p. 128. M. V. Shamolin, Shebarshov D. V. Lagrange tori and equation of Hamilton-Jacobi," In: Book of Abstracts of Conference PDE Prague'98 (Praha, August 1016, 1998; Partial Differential Equations: Theory and Numerical Solutions), Charles University, Praha, Czech Rep. (1998), p. 88. M. V. Shamolin, "New two-parameter families of the phase portraits in threedimensional rigid body dynamics," In: Abstracts of International Conference Dedicated to L. S. Pontryagin's 90th Birthday `Differential Equations,' Moscow, 31.08.6.09, 1998 [in Russian], MGU, Moscow (1998), pp. 9799. M. V. Shamolin, "Lyapunov functions method and many-dimensional topographical systems of Poincare in rigid body dynamics," In: Abstracts of Reports of IV Crimeanian International Mathematical School `Lyapunov Function Method and Its Application,' (LFM-1998), Crimea, Alushta, September 512, 1998 [in Russian], Simpheropol' (1998), p. 80. M. V. Shamolin, "Some classical problems in a three-dimensional dynamics of a

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rigid body interacting with a medium," In: Proc. of ICTACEM'98, Kharagpur, India, Dec. 15, 1998, Aerospace Engineering Dep., Indian Inst. of Technology, Kharagpur, India (1998), p. 11 (CD-Rome, Printed at: Printek Point, Technology Market, KGP-2). M. V. Shamolin, "Integrability in terms of transcendental functions in rigid body dynamics," In: Book of Abstr. of GAMM Annual Meeting, April 1216, 1999, Universite de Metz, Metz, France (1999), p. 144. M. V. Shamolin, "Mathematical modelling of interaction of a rigid body with a medium and new cases of integrability," In: CD-Proc. of ECCOMAS 2000, Barcelona, Spane, September 1114, 2000, Barcelona (2000), p. 11. M. V. Shamolin, "Methods of analysis of dynamics of a rigid body interacting with a medium," In: Book of Abstr. of Annual Scient. Conf. GAMM 2000 at the Univ. of Gottingen, April 27, 2000, Univ. of Gottingen, Gottingen (2000), p. 144. M. V. Shamolin, "Integrability and nonintegrability in terms of transcendental functions," In: CD-Abs. of 3rd ECM (Poster sessions), Barcelona, Spain, June 1014, 2000 (poster No. 36, without pages), Barcelona (2000). M. V. Shamolin, "About interaction of a rigid body with a resisting medium under an assumption of a jet flow," In: Book of Abstr. II (General sessions) of 4th EUROMECH Solid Mech. Conf., Metz, France (June 2630, 2000), Universite de Metz, Metz, France (2000), p. 703. M. V. Shamolin, "New families of many-dimensional phase portraits in dynamics of a rigid body interacting with a medium," In: CD-Proc. of 16th IMACS World Cong. 2000, Lausanne, Switzerland, August 2125, EPFL (2000), p. 3. M. V. Shamolin, "Comparison of some cases of integrability in dynamics of a rigid body interacting with a medium," In: Book of Abstr. of Annual Scient. Conf. GAMM 2001, ETH Zurich, February 1215, 2001, ETH Zurich (2001), p. 132. M. V. Shamolin, "Pattern recognition in the model of the interaction of a rigid body with a resisting medium," In: Col. of Abstr. of First SIAM-EMS Conf. `Applied Mathematics in Our Changing World,' Berlin, Germany, Sept. 26, 2001, Springer, Birkhauser (2001), p. 66. M. V. Shamolin, "Some questions of the qualitative theory of ordinary differential equations and dynamics of a rigid body interacting with a medium," J. Math. Sci., 110, No. 2, 25262555 (2002). MR1919087 (2004j:37161) M. V. Shamolin, "Dynamical systems with the variable dissipation in 3D-dynamics of a rigid body interacting with a medium," In: Book of Abstr. of 4th ENOC, Moscow, Russia, August 1923, 2002 [in Russian], Inst. Probl. Mech. Russ. Acad. Sci., Moscow (2002), p. 109. M. V. Shamolin, "Methods of analysis of dynamics of a 2D-, 3D-, or 4D-rigid body with a medium," In: Abst. Short Commun. Post. Sess. of ICM'2002, Beijing, 2002, August 2028, Higher Education Press, Beijing, China (2002), p. 268. M. V. Shamolin, "New integrable cases and families of portraits in the plane and spatial dynamics of a rigid body interacting with a medium," J. Math. Sci., 114, No. 1, 919975 (2003). MR1965083 (2004d:70008) M. V. Shamolin, "Integrability and nonintegrability in terms of transcendental functions," In: Book of Abstr. of Annual Scient. Conf. GAMM 2003, Abano TermePadua, Italy, March 2428, 2003, Univ. of Padua, Italy (2003), p. 77. M. V. Shamolin, "Global structural stability in dynamics of a rigid body interacting with a medium," In: 5th ICIAM, Sydney, Australia, July 711, 2003, Univ. of Technology, Sydney (2003), p. 306. M. V. Shamolin, "Classes of variable dissipation systems with nonzero mean in the dynamics of a rigid body," J. Math. Sci., 122, No. 1, 28412915 (2004). MR2082898

(2005j:70014) 356. M. V. Shamolin, "Some cases of integrability in dynamics of a rigid body interacting with a resisting medium," In: Abstracts of Reports of International Conference in Differential Equations and Dynamical Systems, Suzdal', July 0510, 2004 [in Russian], Vladimir, Vladimir State University (2004), pp. 296298. 357. M. V. Shamolin, "Mathematical model of interaction of a rigid body with a resisting medium in a jet flow," In: Abstr. Part 1, 76 Annual Sci. Conf. (GAMM), Luxembourg, March 28-April 1, 2005, Univ. du Luxembourg, Luxembourg (2005) pp. 9495. 358. M. V. Shamolin, "Some cases of integrability in 3D dynamics of a rigid body interacting with a medium," In: Book of Abstr. IMA Int. Conf. `Recent Advances in Nonlinear Mechanics,' Aberdeen, Scotland, August 30-September 1, 2005, IMA, Aberdeen (2005), p. 112. 359. M. V. Shamolin, "Almost conservative systems in dynamics of a rigid body," In: Book of Abstr., 77th Annual Meeting of GAMM, March 2731, 2006, Technische Univ. Berlin, Technische Univ., Berlin (2006), p. 74. 360. M. V. Shamolin, "4D-rigid body and some cases of integrability," In: Abstracts of ICIAM07, Zurich, Switzerland, June 1620, 2007, ETH Zurich (2007), p. 311. 361. M. V. Shamolin, "The cases of complete integrability in dynamics of a rigid body interacting with a medium," In: Book of Abstr. of Int. Conf. on the Occasion of the 150th Birthday of A. M. Lyapunov (June 2430, 2007, Kharkiv, Ukraine) [in Russian], Verkin Inst. Low Temper. Physics Engineer. NASU, Kharkiv (2007), pp. 147148. 362. M. V. Shamolin, "On the problem of a symmetric body motion in a resisting medium," In: Book of Abst. of EMAC-2007 (July 14, 2007, Hobart, Australia), Univ. Tasmania, Hobart, Australia (2007), p. 25. 363. M. V. Shamolin, "The cases of integrability in 2D-, 3D-, and 4D-rigid body dynamics," In: Abstr. of Short Commun. and Post, of Int. Conf. `Dynamical Methods and Mathematical Model ling,' Val ladolid, Spane (Sept. 1822, 2007), ETSII, Valladolid (2007), p. 31. 364. M. V. Shamolin, "The cases of integrability in terms of transcendental functions in dynamics of a rigid body interacting with a medium," In: Proc. of 9th Conf. on Dynamical Systems (Theory and Applications) (DSTA 2007), Lodz, Poland, Dec. 1720, 2007, Vol. 1, Tech. Univ. Lodz (2007), pp. 415422. 365. O. P. Shorygin and N. A. Shul'man, "Entrance of a disk to water with angle of arttack," Uch. Zap. TsAGI, 8, No. 1, 1221 (1978). 366. J. L. Singh, Classical Dynamics [Russian translation], Fizmatgiz, Moscow (1963). 367. S. Smale, "Rough systems are not dense," In: A Col lection of Translations. Mathematics [in Russian], 11, No. 4, 107112 (1967). 368. S. Smale, "Differentiable dynamical systems," Usp. Mat. Nauk, 25, No. 1, 113185 (1970). MR0263116 (41 #7721) 369. V. M. Starzhinskii, Applied Methods of Nonlinear Oscil lations [in Russian], Nauka, Moscow (1977). MR0495355 (58 #14067) 370. V. A. Steklov, On Rigid Body Motion in a Fluid [in Russian], Khar'kov (1893). 371. V. V. Stepanov, A Course of Differential Equations [in Russian], Fizmatgiz, Moscow (1959). 372. E. I. Suvorova and M. V. Shamolin, "Poincarґ topographical systems and compare ison systems of higher orders," In: Mathematical Conference `Modern Methods of Function Theory and Related Problems,' Voronezh, January 26-February 2, 2003 [in Russian], Voronezh State University, Voronezh (2003), pp. 251252. 373. G. K. Suslov, Theoretical Mechanics [in Russian], Gostekhizdat, Moscow (1946).

374. V. V. Sychev, A. I. Ruban, and G. L. Korolev, Asymptotic Theory of Separation Flows [In Russian], Nauka, Moscow (1987). 375. V. G. Tabachnikov, "Stationary characteristics of wings in small velocities under whole range of angles of attack," In: Proceedings of Central Aero-Hydrodynamical Institute [in Russian], Issue 1621, Moscow (1974), pp. 1824. 376. Ya. V. Tatarinov, Lectures on Classical Dynamics [in Russian], MGU, Moscow (1984). 377. V. V. Trofimov, "Embeddings of finite groups in compact Lie groups by regular elements," Dokl. Akad. Nauk SSSR, 226, No. 4, 785786 (1976). MR0439984 (55 #12865) 378. V. V. Trofimov, "Euler equations on finite-dimensional solvable Lie groups," Izv. Akad. Nauk SSSR, Ser. Mat., 44, No. 5, 11911199 (1980). MR0595263 (82e:70006) 379. V. V. Trofimov, "Symplectic structures on automorphism groups of symmetric spaces," Vestn. MGU, Ser. 1, Mat., Mekh., 6, 3133 (1984). MR0775300 (86b:53038) 380. V. V. Trofimov, "Geometric invariants of completely integrable systems," In: Abstract of Reports of Al l-Union Conference in Geometry in the `Large,' Novosibirsk (1987), p. 121. 381. V. V. Trofimov and A. T. Fomenko, " A methodology for constructing Hamiltonian flows on symmetric spaces and integrability of certain hydrodynamic systems," Dokl. Akad. Nauk SSSR, 254, No. 6, 13491353 (1980). MR0592507 (82b:58038) 382. V. V. Trofimov and M. V. Shamolin, "Dissipative systems with nontrivial generalized Arnol'd-Maslov classes," In: Abstracts of Reports of Workshop in Vector and Tensor Analysis Named after P. K. Rashevskii, Vestn. MGU, Ser. 1, Mat., Mekh. 2, 62 (2000). 383. Ch. J. De La Vallee Poussin, Lectures on Theoretical Mechanics, Vols. I, II [Russian translation], IL, Moscow (19481949). 384. S. V. Vishik and S. F. Dolzhanskii, "Analogs of Euler-Poisson equations and magnetic electrodynamic related to Lie groups," Dokl. Akad. Nauk SSSR, 238, No. 5, 10321035. 385. I. N. Vrublevskaya, "On geometric equivalence of tra jectories and semitra jectories of dynamical systems," Mat. Sb., 42 (1947). 386. I. N. Vrublevskaya, "Some criteria of equivalence of tra jectories and semitra jectories of dynamical systems," Dokl. Akad. Nauk SSSR, 97, No. 2 (1954). MR0067480 (16,734i) 387. C.-L. Weyher, Observations sur le Vol Plane Par Obres, "L'Aeronaute" (1890). 388. E. T. Whittecker, Analytical Dynamics [Russian translation], ONTI, Moscow (1937). 389. M. V. Yakobson, "On self-mappings of a circle," Mat. Sb., 85, 183188 (1975). 390. N. E. Zhukovskii, "On a fall of light oblong bodies rotating around their longitudinal axis," In: A Complete Col lection of Works [in Russian], Vol. 5, Fizmatgiz, Moscow (1937), pp. 7280, 100115. 391. N. E.. Zhukovskii, "On bird soaring," In: A Complete Col lection of Works [in Russian] Vol. 5, Fizmatgiz, Moscow (1937), pp. 4959. 392. V. F. Zhuravlev and D. M. Klimov, Applied Methods in Oscil lation Theory [in Russian], Nauka, Moscow (1988). MR0987633 (90g:70001) 393. Yu. F. Zhuravlev, "Submergence of a disk into a fluid at an angle to a free surface," In: A Col lection of Works in Hydrodynamics [in Russian], Central AeroHydrodynamical Institute, Moscow (1959), pp. 164167.
Note: This list reflects references listed in the original paper as accurately as possible with no attempt to correct errors.

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MR2676327 (2011i:16057) 16T25 16W50 A idagulov, R. R. (RS-MOSC) ; Shamolin, M. V. (RS-MOSC) Color groups. (Russian. Russian summary)

Sovrem. Mat. Prilozh. No. 62, Geometriya i Mekhanika (2009), 1426; translation in J. Math. Sci. (N. Y.) 161 (2009), no. 5, 615627. In this investigative review the authors aim to define groups of colors, elaborating on what kind of groups can belong to such color groups and how they should differ from the graded subgroups. Much emphasis is placed on the Yang-Baxter symmetry, which has been shown to play a crucial role in describing the notion of a true color group. The central concept is explained in a systematic way through several definitions, statements and their proofs. The notion of the color group is shown to be related to the grading over the algebra, which in turn is linked also to the symmetry and the solution of the YangBaxter relation. The subtle difference between the grading of a group and a colored group is explained by introducing the notion of bicharacter. It is emphasized through several steps that, to every grading element g , a color can be assigned constituting a set of equivalent g -grading with the bicharacter depending only on the color group and not on the empty part of the grading. As an illuminating example, the well-known Clifford algebra is shown to be a color algebra of a color group. Anjan Kundu
References

1. L. N. Balaba and S. A. Pikhtil'kov, "Primary radical of special Lie superalgebras," Fundam. Prikl. Mat., 9, No. 1, 5160 (2003). 2. Kh. Bass, Algebraic K -Theory [Russian translation], Mir, Moscow (1973). MR0346032 (49 #10758) 3. I. Bukur and A. Delyanu, Introduction to the Theory of Categories and Functors [Russian translation], Mir, Moscow (1972). MR0349790 (50 #2283) 4. Ch. Curtis and I. Rayner, The Representation Theory of Finite Groups and Associative Algebras [Russian translation] (S. D. Berman (Ed.)), Nauka, Moscow (1969). MR0248238 (40 #1490) 5. E. E. Demidov, Quantum Groups [in Russian], Faktorial, Moscow (1998). 6. V. G. Drinfel'd, "Hopf algebras and the quantum Young-Baxter equation," Dokl. Akad. Nauk SSSR, 283, No. 5, 10601064 (1985). MR0802128 (87h:58080) 7. V. G. Drinfel'd, "Quantum groups," Zap. Nauch. Semin LOMI, 155, 1949 (1986). 8. K. Feis, Algebra: Rings, Modules, and Categories [in Russian] (L. A. Skornyakov (Ed.)), Vol. I, Mir, Moscow (1977). MR0491784 (58 #10983) 9. A. T. Fomenko, Symplectic Geometry: Methods and Applications [in Russian], MGU, Moscow (1988). MR0964470 (90k:58082) 10. General Algebra [in Russian] (L. A. Skornyakov (Ed.)), Vols. 12, Nauka, Moscow (1990). MR1137273 (93a:00001a) 11. M. V. Gross, D. Huybrechts, D. Joice, "Calabi-Yau manifolds and related geometries," In: Lectures at a Summer School in Nordfjordeid, Norway, June 2001, Berlin etc.: Springer, Cop., VIII (2003), pp. 299. MR1963562 12. D. Huesmuller, Stratified Spaces [Russian translation], Mir, Moscow (1970). 13. K. Kassel, Quantum Groups [Russian translation], Fazis, Moscow (1999). 14. B. A. Kupershmidt, "KP or mKP: non-commutative mathematics of Lagrangian, Hamiltonian, and integrable systems," In: Moscow-Izhevsk, Reg. Chaot. Dynam.

[Russian translation], Moscow-Izhevsk (2002), pp. 1612. MR1752088 (2001d:37113) 15. S. MacLane, Categories for Working Mathematician [Russian translation], Fizmatlit, Moscow (2004). 16. A. A. Mikhalev, "Subalgebras of free colored Lie Superalgebras," Mat. Zametki, 37, No. 5, 653659 (1985). MR0797705 (87a:17023) 17. V. Nazaikinskii, B. Sternin, and V. Shatalov, Methods of Non-commutative Analysis [in Russian], Tekhnosfera, Moscow (2002). 18. S. P. Novikov and I. A. Taimanov, Modern Geometric Structures and Fields [in Russian], MTsNMO, Moscow (2005). MR2264644 (2007i:53001) 19. Roger Penrose, "A way to the reality or laws ruling over the universe," In: MoscowIzhevsk, Reg. and Chaot. Dynam. [Russian translation], Moscow-Izhevsk (2007). 20. A. Poincarґ On Curves Defined by Differential Equations [Russian translation], e, Gostekhizdat, Moscow-Leningrad (1947). 21. A. Poincarґ New Methods in Celestial Mechanics [Russian translation], Selected e, Works, Vol. 1. Nauka, Moscow (1971); Vol. 2. Nauka, Moscow (1972). 22. M. Sh. Tsalenko and E. G. Schulgeifer, Basics of the Theory of Categories [in Russian], Nauka, Moscow (1974). 23. I. R. Shafarevich, Basic Notions of Algebra [in Russian], Izhevsk (2001). 24. M. V. Shamolin, "New integrable cases and families of portraits in the plane and spatial dynamics of a rigid body interacting with a medium," J. Math. Sci., 114, No. 1, 919975 (2003). MR1965083 (2004d:70008) 25. M. V. Shamolin, "Classes of variable dissipation systems with nonzero mean in the dynamics of a rigid body," J. Math. Sci., 122, No. 1, 28412915 (2004). MR2082898 (2005j:70014) 26. Yu. Vladimirov, Geometrophysics [in Russian], Binom, Moscow (2005).
Note: This list reflects references listed in the original paper as accurately as possible with no attempt to correct errors.

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MR2541122 (2010k:70007) 70E15 70H06 Shamolin, M. V. (RS-MOSC-IMC) New cases of complete integrability in the dynamics of a dynamically symmetric four-dimensional rigid b o dy in a nonconservative field. (Russian) Dokl. Akad. Nauk 425 (2009), no. 3, 338342.

Two conditional integrable cases are constructed in the dynamics of a 4-dimensional axisymmetric rigid body moving under the action of a resistance-like follower-force applied to a certain specially chosen point on the body. Two types of axial symmetry are considered, in which the inertia matrix has three (or two pairs of ) equal eigenvalues. The dynamics is shown to be integrable on the intersection of three (or two) invariant hyperplanes of the space of angular velocities. Hamad Mohamed Yehia c Copyright American Mathematical Society 2010, 2015

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MR2517009 (2010b:37158) 37J35 70H06 Shamolin, M. V. On the integrability in elementary functions of some classes of dynamical systems. (Russian. Russian summary) Vestnik Moskov. Univ. Ser. I Mat. Mekh. 2008, no. 3, 4349, 72.

From the text (translated from the Russian): "The results of this paper are due to a previous investigation of the applied problem of the motion of a rigid body in a resisting medium [V. A. Samsonov and M. V. Shamolin, Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1989, no. 3, 5154, 105; MR1029730 (90k:70007)] in which a transcendental integral expressed in terms of elementary functions was obtained for a particular case. This made it possible to carry out a complete analysis of phase tra jectories and to indicate those properties that were `robust' and preserved for some more general systems. The integrability of the system in [op. cit.] is related to latent symmetries. Therefore, it is of interest to study sufficiently large classes of dynamical systems with such latent symmetries." c Copyright American Mathematical Society 2010, 2015

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MR2482029 (2010f:37032) 37C10 34A05 37J35 70H05 Shamolin, M. V. (RS-MOSC) Dynamical systems with variable dissipation: approaches, metho ds, and applications.2076-6203 (Russian. English, Russian summaries) Fundam. Prikl. Mat. 14 (2008), no. 3, 3237; translation in J. Math. Sci. (N. Y.) 162

(2009), no. 6, 741908. Summary: "This work is devoted to the development of qualitative methods in the theory of nonconservative systems that arise, e.g., in such fields of science as the dynamics of a rigid body interacting with a resisting medium, oscillation theory, etc. This material can attract the interest of specialists in the qualitative theory of ordinary differential equations, in rigid body dynamics, as well as in fluid and gas dynamics since the work uses the properties of motion of a rigid body in a medium under the streamline flow around conditions. "The author obtains a full spectrum of complete integrability cases for nonconservative dynamical systems having nontrivial symmetries. Moreover, in almost all cases of integrability, each of the first integrals is expressed through a finite combination of elementary functions and is a transcendental function of its variables, simultaneously. In this case, the transcendence is meant in the complex analytic sense, i.e., after the continuation of the functions considered to the complex domain, they have essentially singular points. The latter fact is stipulated by the existence of attracting and repelling limit sets in the system considered (for example, attracting and repelling foci).

"The author obtains new families of phase portraits of systems with variable dissipation on lower- and higher-dimensional manifolds. He discusses the problems of their absolute or relative roughness. He discovers new integrable cases of the rigid body motion, including those in the classical problem of motion of a spherical pendulum placed in the over-running medium flow." A. P. Sadovski i
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Technical Information, Moscow (1989). 246. V. A. Samsonov, B. Ya. Lokshin, and V. A. Privalov, "Qualitative analysis," in: Scientific Report of Institute of Mechanics, Moscow State Univ., No. 3245 [in Russian], Institute of Mechanics, Moscow State Univ., Moscow (1985). 247. V. A. Samsonov and M. V. Shamolin, "On body motion in a resisting medium," in: Contemporary Problems of Mechanics and Technologies of Machine Industry, Al l-Union Conf., April 1618, 1989. Abstracts of Reports [in Russian], All-Union Institute for Scientific and Technical Information, Moscow (1989), pp. 128129. 248. V. A. Samsonov and M. V. Shamolin, "To problem on body motion in a resisting medium," Vestn. Mosk. Univ. Ser. 1 Mat. Mekh., No. 3, 5154 (1989). MR1029730 (90k:70007) 249. V. A. Samsonov and M. V. Shamolin, "A model problem of body motion in a medium with streamline flow-around," Scientific Report of Institute of Mechanics, Moscow State Univ. [in Russian], No. 3969, Institute of Mechanics, Moscow State Univ., Moscow (1990). 250. V. A. Samsonov and M. V. Shamolin, "A model problem of body motion in a medium with streamline flow-around," in: Nonlinear Oscil lations of Mechanical Systems, Abstracts of Reports of II Al l-Union Conf., September, 1990, Pt. 2 [in Russian], Gor'kii (1990), pp. 9596. 251. V. A. Samsonov and M. V. Shamolin, "To problem of body drag in a medium under streamline flow-around," in: Scientific Report of Institute of Mechanics, Moscow State Univ., No. 4141 [in Russian], Institute of Mechanics, Moscow State Univ., Moscow (1991). 252. V. A. Samsonov and M. V. Shamolin, "On stability of a body under its drag in a resisting medium," in: VII Chetaev Conf. "Analytical Mechanics, Stability, and Control of Motion," June 1013, 1997. Abstracts of Reports, Kazan' State Technical Univ., Kazan' (1997), p. 24. 253. V. A. Samsonov, M. V. Shamolin, V. A. Eroshin, and V. M. Makarshin, "Mathematical modelling in problem of body drag in a resisting medium under streamline flow-around," in: Scientific Report of Institute of Mechanics, Moscow State Univ., No. 4396 [in Russian], Moscow (1995). 254. G. Sansone, Ordinary Differential Equations [Russian translation], Inostr. Lit., Moscow (1954). 255. L. I. Sedov, Mechanics of Continuous Media [in Russian], Vols., 1, 2, Nauka, Moscow (1983, 1984). 256. H. Seifert and W. Threifall, Topology [Russian translation], Gostekhizdat, Moscow (1938). 257. N. Yu. Selivanova and M. V. Shamolin, "Extended Cahn-Hilliard model and certain of its solutions," in: Materials of Voronezh Al l-Russian Conf. "Pontryagin Readings--XVIII," Voronezh, May, 2007, Voronezh State Univ., Voronezh (2007), pp. 145146. 258. J. L. Singh, Classical Dynamics [Russian translation], Fizmatgiz, Moscow (1963). 259. M. V. Shamolin, Qualitative Analysis of a Model Problem of Body Motion in a Medium with Streamline Flow-Around [in Russian], Candidate Dissertation, MGU, Moscow (1991). 260. M. V. Shamolin, Qualitative Analysis of a Model Problem of Body Motion in a Medium with Streamline Flow-Around [in Russian], Theses of Candidate Dissertation, MGU, Moscow (1991). 261. M. V. Shamolin, "Closed tra jectories of different topological types in problem of body motion in a medium with resistance," Vestn. Mosk. Univ. Ser. 1 Mat. Mekh., No. 2, 5256 (1992). MR1293705 (95d:34060)

262. M. V. Shamolin, "To problem of body motion in a medium with resistance," Vestn. Mosk. Univ. Ser. 1 Mat. Mekh., No. 1, 5258 (1992). MR1214592 (93k:70028) 263. M. V. Shamolin, "A new two-parameter family of phase portaits for problem of a body motion in a resisting medium," in: Model ling and Study of Stability of Systems, Sci. Conf., May 2428, 1993. Abstracts of Reports, Pt. 2 [in Russian], Znanie, Kiev (1993), pp. 6263. 264. M. V. Shamolin, "Applications of Poincarґ topographical system methods and e comparison systems in some concrete systems of differential equations," Vestn. Mosk. Univ. Ser. 1 Mat. Mekh., No. 2, 6670 (1993). MR1223987 (94b:34060) 265. M. V. Shamolin, "Classification of phase portraits in problem of body motion in a resisting medium in the presence of a linear damping moment," Prikl. Mat. Mekh., 57, No. 4, 4049 (1993). MR1258007 (94i:70027) 266. M. V. Shamolin, "Existence and uniqueness of tra jectories having infinitely distant points as limit sets for dynamical systems on a plane," Vestn. Mosk. Univ. Ser. 1 Mat. Mekh., No. 1, 6871 (1993). MR1293942 (95e:34036) 267. M. V. Shamolin, "Global qualitative analysis of nonlinear systems on the problem of a body motion in a resisting medium," in: Fourth Col loquium on the Qualitative Theory of Differential Equations, Bolyai Institute, August 1821, 1993, Szeged, Hungary (1993), p. 54. 268. M. V. Shamolin, "Relative structural stability of problem of body motion in a resisting medium," in: Mechanics and Its Applications, Sci. Conf., November 911, 1993, Abstracts of Reports, Tashkent State Univ., Tashkent (1993), pp. 2021. 269. M. V. Shamolin, "A new two-parameter family of phase portraits in problem of a body motion in a medium," Dokl. Ross. Akad. Nauk, 337, No. 5, 611614 (1994). MR1298329 (95g:70006) 270. M. V. Shamolin, "On relative roughness of dynamical systems in problem of body motion in a medium under streamline flow around," in: Model ling and Study Stability of Systems, Sci. Conf., May 1620, 1994. Abstract of Reports [in Russian], Kiev (1994), pp. 144145. 271. M. V. Shamolin, "Relative structural stability on the problem of a body motion in a resisting medium," in: ICM'94, Abstract of Short Communications, Zurich, 311 August, 1994, Zurich, Switzerland (1994), p. 207. 272. M. V. Shamolin, "A new two-parameter family of phase portraits with limit cycles in rigid body dynamics interacting with a medium," in: Model ling and Study of Stability of Systems, Sci. Conf., May 1519, 1995. Abstracts of Reports (Study of Systems) [in Russian], Kiev (1995), p. 125. 273. M. V. Shamolin, "New two-parameter families of the phase patterns on the problem of a body motion in a resisting medium," in: ICIAM'95, Book of Abstracts. Hamburg, 37 July, 1995, Hamburg, Germany (1995), p. 436. 274. M. V. Shamolin, "On relative structural stability of dynamical systems in problem of body motion in a resisting medium," the abstract of a talk at the Chebyshev Readings, Vestn. Mosk. Univ. Ser. 1 Mat Mekh., No. 6, 17 (1995). MR1809236 275. M. V. Shamolin, "Poisson-stable and dense orbits in rigid body dynamics," in: 3rd Experimental Chaos Conf., Advance Program. Edinburgh, Scotland, August 2123, 1995, Edinburgh, Scotland (1995), p. 114. 276. M. V. Shamolin, "Qualitative methods to the dynamic model of interaction of a rigid body with a resisting medium and new two-parametric families of the phase portraits," in: DynDays'95 (Sixteenth Annual Informal Workshop), Program and Abstracts. Lyon, June 28-July 1, 1995, Lyon, France (1995), p. 185. 277. M. V. Shamolin, "Relative structural stability of dynamical systems for problem of body motion in a medium," in: Analytical, Numerical, and Experimental Methods in

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Mechanics. A Col lection of Scientific Works [in Russian], Izd. Mosk. Univ., Moscow (1995), pp. 1419. MR1809236 M. V. Shamolin, "Structural optimization of the controlled rigid motion in a resisting medium," in: WCSMO-1, Extended Abstracts. Posters. Goslar, May 28-June 2, 1995, Goslar, Germany (1995), p. 1819. M. V. Shamolin, "A list of integrals of dynamical equations in spatial problem of body motion in a resisting medium," in: Model ling and Study of Stability of Systems, Sci. Conf., May 2024, 1996. Abstracts of Reports (Study of Systems) [in Russian], Kiev (1996), p. 142. M. V. Shamolin, "Definition of relative roughness and two-parameter family of phase portraits in rigid body dynamics," Usp. Mat. Nauk, 51, No. 1, 175176 (1996). MR1392692 (97f:70010) M. V. Shamolin, "Introduction to problem of body drag in a resisting medium and a new two-parameter family of phase portraits," Vestn. Mosk. Univ. Ser. 1 Mat. Mekh., No. 4, 5769 (1996). MR1644665 (99e:70027) M. V. Shamolin, "Introduction to spatial dynamics of rigid body motion in resisting medium," in: Materials of Int. Conf. and Chebyshev Readings Devoted to the 175th Anniversary of P. L. Chebyshev, Moscow, May 1419, 1996, Vol. 2 [in Russian], Izd. Mosk. Univ., Moscow (1996), pp. 371373. M. V. Shamolin, "On a certain integrable case in dynamics of spatial body motion in a resisting medium," in: II Symposium in Classical and Celestial Mechanics. Abstracts of Reports. Velikie Luki, August 2328, 1996 [in Russian], Moscow-Velikie Luki (1996), pp. 9192. M. V. Shamolin, "Periodic and Poisson stable tra jectories in problem of body motion in a resisting medium," Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 2, 5563 (1996). M. V. Shamolin, "Qualitative methods in dynamics of a rigid body interacting with a medium," in: II Siberian Congress in Applied and Industrial Mathematics, Novosibirsk, June 2530, 1996. Abstracts of Reports, Pt. III [in Russian], Novosibirsk (1996), p. 267. M. V. Shamolin, "Qualitative methods in interacting with the medium rigid body dynamics," in: Abstracts of GAMM Wissenschaftliche Jahrestagung'96, 27.-31. May, 1996, Czech Rep., Karls-UniversitЁ Prag., Prague (1996), pp. 129130. at M. V. Shamolin, "Qualitative methods in interacting with the medium rigid body dynamics," in: Abstracts of XIXth ICTAM, Kyoto, Japan, August 2531, 1996, Kyoto, Japan (1996), p. 285. M. V. Shamolin, "Relative structural stability and relative structural instability of different degrees in topological dynamics," in: Abstracts of Int. Topological Conf. Dedicated to P. S. Alexandroff 's 100th Birthday "Topology and Applications," Moscow, May 2731, 1996, Fazis, Moscow (1996), pp. 207208. M. V. Shamolin, "Spatial Poincarґ topographical systems and comparison systems," e in: Abstract of Reports of Math. Conf. "Erugin Readings," Brest, May 1416, 1996 [in Russian], Brest (1996), p. 107. MR1479402 (99a:34089) M. V. Shamolin, "Topographical Poincarґ systems in many-dimensional spaces," e in: Fifth Col loquium on the Qualitative Theory of Differential Equations, Bolyai Institute, Regional Committee of the Hungarian Academy of Sciences, July 29August 2, 1996, Szeged, Hungary (1996), p. 45. M. V. Shamolin, "Variety of types of phase portraits in dynamics of a rigid body interacting with a resisting medium," Dokl. Ross. Akad. Nauk, 349, No. 2, 193197 (1996). MR1440994 (98b:70009)

293. M. V. Shamolin, "Classical problem of a three-dimensional motion of a pendulum in a jet flow," in: 3rd EUROMECH Solid Mechanics Conf., Book of Abstracts, Stockholm, Sweden, August 1822, 1997, Royal Inst. of Technology, Stockholm, Sweden (1997), p. 204. 294. M. V. Shamolin, "Families of three-dimensional phase portraits in dynamics of a rigid body," in: EQUADIFF 9, Abstracts, Enlarged Abstracts, Brno, Czech Rep., August 2529, 1997, Masaryk Univ., Brno, Czech Rep. (1997), p. 76. 295. M. V. Shamolin, "Jacobi integrability of problem of a spatial pendulum placed in over-running medium flow," in: Model ling and Investigation of System Stability. Sci. Conf., May 1923, 1997. Abstracts of Reports [in Russian], Kiev (1997), p. 143. 296. M. V. Shamolin, "Mathematical modelling of dynamics of a spatial pendulum flowing around by a medium," in Proc. of VII Int. Symposium "Methods of Discrete Singularities in Problems of Mathematical Physics," Feodociya, June 2629, 1997 [in Russian], Kherson State Technical Univ., Kherson (1997), pp. 153154. 297. M. V. Shamolin, "On an integrable case in spatial dynamics of a rigid body interacting with a medium," Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 2, 6568 (1997). 298. M. V. Shamolin, "Partial stabilization of body rotational motions in a medium under a free drag," Abstracts of Reports of Al l-Russian Conf. with Int. Participation "Problems of Celestial Mechanics," St. Petersburg, June 36, 1997 [in Russian], Institute of Theoretical Astronomy, Russian Academy of Sciences, St. Petersburg (1997), pp. 183184. 299. M. V. Shamolin, "Qualitative methods in dynamics of a rigid body interacting with a medium," in: YSTM'96: "Young People, the Third Mil lenium," Proc. of Int. Congress (Ser. Professional) [in Russian], Vol. 2, NTA "APFN," Moscow (1997), pp. 14. 300. M. V. Shamolin, "Spatial dynamics of a rigid body interacting with a medium," Workshop in Mechanics of Systems and Problems of Motion Control and Navigation, Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 4, 174 (1997). 301. M. V. Shamolin, "Spatial Poincarґ topographical systems and comparison systems," e Usp. Mat. Nauk, 52, No. 3, 177178 (1997). MR1479402 (99a:34089) 302. M. V. Shamolin, "Three-dimensional structural optimization of controlled rigid motion in a resisting medium," in: Proc. of WCSMO-2, Zakopane, Poland, May 2630, 1997, Zakopane, Poland (1997), pp. 387392. 303. M. V. Shamolin, "Three-dimensional structural optimization of controlled rigid motion in a resisting medium," in: WCSMO-2, Extended Abstracts, Zakopane, Poland, May 2630, 1997, Zakopane, Poland (1997), pp. 276277. 304. M. V. Shamolin, "Absolute and relative structural stability in spatial dynamics of a rigid body interacting with a medium," in: Proc. of Int. Conf. "Mathematics in Industry," ICIM-98, Taganrog, June 29-July 3, 1998 [in Russian], Taganrog State Pedagogical Inst., Taganrog (1998), pp. 332333. 305. M. V. Shamolin, "Families of portraits with limit cycles in plane dynamics of a rigid body interacting with a medium," Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 6, 2937 (1998). 306. M. V. Shamolin, "Family of three-dimensional phase portraits in spatial dynamics of a rigid body interacting with a medium," in: III Int. Symposium in Classical and Celestial Mechanics, August 2327, 1998, Velikie Luki. Abstracts of Reports [in Russian]. Computational Center of Russian Academy of Sciences, Moscow-Velikie Luki (1998), pp. 165167. 307. M. V. Shamolin, "Lyapunov functions method and many-dimensional topographical systems of Poincarґ in rigid body dynamics," in: Abstract of Reports of IV Crimee

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nian Int. Math. School "Lyapunov Function Method and Its Applications," Crimea, Alushta, September 512, Simpheropol' State Univ., Simpheropol' (1998), p. 80. M. V. Shamolin, "Many-dimensional topographical Poincarґ systems in rigid body e dynamics," in: Abstracts of GAMM Wissenschaftliche Jahrestagung'98, 6.-9. April, 1998, UniversitЁ Bremen, Bremen, Germany (1998), p. 128. at M. V. Shamolin, "Methods of nonlinear analysis in dynamics of a rigid body interacting with a medium," in: Abstracts of Reports of Int. Congress "Nonlinear Analysis and Its Applications," Moscow, September 15, 1988 [in Russian], Moscow (1998), p. 131. M. V. Shamolin, "Methods of nonlinear analysis in dynamics of a rigid body interacting with a medium," in: CD-Proc. of the Congress "Nonlinear Analysis and Its Applications," Moscow, Russia, September 15, 1998, Moscow (1999), pp. 497508. M. V. Shamolin, "New two-parametric families of the phase portraits in threedimensional rigid body dynamics," in: Int. Conf. Devoted to the 90th Anniversary of L. S. Pontryagin, Moscow, August 31-September 6, 1998, Abstract of Reports, Differntial Equations, Izd. Mosk. Univ., Moscow (1998), pp. 9799. M. V. Shamolin, "On integrability in transcendental functions," Usp. Mat. Nauk, 53, No. 3, 209210 (1998). MR1657632 (99h:34006) M. V. Shamolin, "Qualitative and numerical methods in some problems of spatial dynamics of a rigid body interacting with a medium," in: Abstracts of Reports of 5th Int. Conf.-Workshop "Engineering-Physical Problems of New Tehnics," Moscow, May 1922, 1998 [in Russian], Moscow State Technical Univ., Moscow (1998), pp. 154155. M. V. Shamolin, "Some classical problems in three-dimensional dynamics of a rigid body interacting with a medium," in: Proc. of ICTACEM'98, Kharagpur, India, December 15, 1998, Aerospace Engineering Dep., Indian Inst. of Technology, Kharagpur, India (1998), p. 11. M. V. Shamolin, "Some problems of spatial dynamics of a rigid body interactng with a medium under quasi-stationarity conditions," in: Abstracts of Reports of Al lRussian Sci.-Tech. Conf. of Young Scientists "Modern Problems of Aero-Cosmos Science," Zhukovskii, May 2729, 1998 [in Russian], Central Aero-Hydrodynamical Inst., Moscow (1998), pp. 8990. M. V. Shamolin, "Certain classes of partial solutions in dynamics of a rigid body interacting with a medium," Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 2, 178189 (1999). M. V. Shamolin, "Families of long-period tra jectories in spatial dynamics of a rigid body," in: Model ling and Study of Stability of Systems, Sci. Conf., May 2529 1999. Abstracts of Reports [in Russian], Kiev (1999), p. 60. M. V. Shamolin, "Integrability in terms of transcendental functions in rigid body dynamics," in: Book of Abstracts of GAMM Annual Meeting, April 1216, 1999, Metz, France, Universitґ de Metz, Metz, France (1999), p. 144. e M. V. Shamolin, "Long-periodic tra jectories in rigid body dynamics," in: Sixth Col loquium on the Qualitative Theory of Differential Equations, Bolyai Institute, Regional Committee of the Hungarian Academy of Sciences, August 1014, 1999, Szeged, Hungary (1999), p. 47. M. V. Shamolin, "Mathematical modelling in 3D dynamics of a rigid interacting with a medium," in: Book of Abstracts of the Second Int. Conf. "Tools for Mathematical Model ling," Saint-Petersburg, Russia, 1419 June, 1999, Saint-Petersburg State Tech. Univ., Saint-Petersburg (1999), pp. 122123. M. V. Shamolin, "Methods of analysis of a deceleration of a rigid in 3D medium,"

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in: Contributed Abstracts of 3rd ENOC, Copenghagen (Lyngby), Denmark, August 812, 1999, Tech. Univ. of Denmark, Copenghagen (1999). M. V. Shamolin, "New families of the nonequivalent phase portraits in 3D rigid body dynamics," in: Abstracts of Second Congress ISAAC 1999, Fukuoka, Japan, August 1621, 1999, Fukuoka Ins. of Tech., Fukuoka (1999), pp. 205206. M. V. Shamolin, "New Jacobi integrable cases in dynamics of a rigid body interacting with a medium," Dokl. Ross. Akad. Nauk, 364, No. 5, 627629 (1999). MR1702618 (2000k:70008) M. V. Shamolin, "Nonlinear dynamical effects in spatial body drag in a resisting medium," in: Abstracts of Reports of III Int. Conf. "Chkalov Readings, EngineeringPhysical Problems of Aviation and Cosmos Technics" (June 14, 1999) [in Russian], EATK GA, Egor'evsk (1999), pp. 257258. M. V. Shamolin, "On roughness of dissipative systems and relative roughness and nonroughness of variable dissipation systems," Usp. Mat. Nauk, 54, No. 5, 181182 (1999). MR1741681 (2000j:37021) M. V. Shamolin, "Properties of integrability of systems in terms of transcendental functions," in: Final Progr. and Abstracts of Fifth SIAM Conf. on Appl. of Dynamic. Syst., May 2327, 1999, Snowbird, Utah, USA, SIAM (1999), p. 60. M. V. Shamolin, "Some properties of transcendental integrable dynamical systems," in: Book of Abstracts of EQUADIFF 10, Berlin, August 17, 1999, Free Univ. of Berlin, Berlin (1999), pp. 286287. M. V. Shamolin, "Structural stability in 3D dynamics of a rigid body," in: WCSMO3, Short Paper Proc., Buffalo, NY, May 1721, 1999, Vol. 2, Buffalo (1999), pp. 475477. M. V. Shamolin, "Structural stability in 3D dynamics of a rigid body," in: CD-Proc. of WCSMO-3, Buffalo, NY, May 1721, 1999, Buffalo (1999), p. 6. M. V. Shamolin, "A new family of phase portraits in spatial dynamics of a rigid body interacting with a medium," Dokl. Ross. Akad. Nauk, 371, No. 4, 480483 (2000). MR1776307 (2001k:70006) M. V. Shamolin, "About interaction of a rigid body with a resisting medium under an assumption of a jet flow," in: Book of Abstracts II (General sessions) of 4th EUROMECH Solid. Mech. Conf., Metz, France (June 2630, 2000), Univ. of Metz (2000), p. 703. M. V. Shamolin, "Comparison of certain integrability cases from two-, three-, and four-dimensional dynamics of a rigid body interacting with a medium," in: Abstracts of Reports of V Crimeanian Int. Math. School "Lyapunov Function Method and Its Application," (MLF-2000), Crimea, Alushta, September 513, 2000 [in Russian], Simpheropol' (2000), p. 169. M. V. Shamolin, "Integrability and nonintegrability in terms of transcendental functions," in: CD-Abstracts of 3rd ECM (Poster sessions), Barcelona, Spain, June 1014, 2000, Poster No. 36. M. V. Shamolin, "Jacobi integrability of problem of four-dimensional body motion in a resisting medium," in: Abstracts of Reports of Int. Conf. in Differential Equations and Dynamical Systems, Suzdal', August 2126, 2000 [in Russian], Vladimir State Univ., Vladimir (2000), pp. 196197. M. V. Shamolin, "Jacobi integrability in problem of four-dimensional rigid body motion in a resisting medium," Dokl. Ross. Akad. Nauk, 375, No. 3, 343346 (2000). MR1833828 (2002c:70005) M. V. Shamolin, "Many-dimensional Poincarґ systems and transcendental integrae bility," in: IV Siberian Congress in Applied and Industrial Mathematics, Novosibirsk, June 26-July 1, 2000. Abstracts of Reports, Pt. I [in Russian], Novosibirsk,

Institute of Mathematics (2000), pp. 2526. 337. M. V. Shamolin, "Mathematical modelling of interaction of a rigid body with a medium and new cases of integrability," In: Book of Abstracts of ECCOMAS 2000, Barcelona, Spain, 1114 September, Barcelona (2000), p. 495. 338. M. V. Shamolin, "Mathematical modelling of interaction of a rigid body with a medium and new cases of integrability," in: CD-Proc. of ECCOMAS 2000, Barcelona, Spain, 1114 September, Barcelona (2000), p. 11. 339. M. V. Shamolin, "Methods of analysis of dynamics of a rigid body interacting with a medium," in: Book of Abstracts of Annual Sci. Conf. GAMM 2000 at the Univ. of GЁ ottingen, 27 April, 2000, Univ. of GЁ ottingen (2000), p. 144. 340. M. V. Shamolin, "New families of many-dimensional phase portraits in dynamics of a rigid body interacting with a medium," in: Book of Abstracts of 16th IMACS World Congress 2000, Lausanne, Switzerland, August 2125, 2000, EPFL (2000), p. 283. 341. M. V. Shamolin, "New families of many-dimensional phase portraits in dynamics of a rigid body interacting with a medium," in: CD-Proc. of 16th IMACS World Congress 2000, Lausanne, Switzerland, August 2125, 2000, EPFL (2000). 342. M. V. Shamolin, "On a certain case of Jacobi integrability in dynamics of a fourdimensional rigid body interacting with a medium," in: Abstracts of Reports of Int. Conf. in Differential and Integral Equations, Odessa, September 1214, 2000 [in Russian], AstroPrint, Odessa (2000), pp. 294295. 343. M. V. Shamolin, "On limit sets of differential equations near singular points," Usp. Mat. Nauk, 55, No. 3, 187188 (2000). MR1777365 (2002d:34049) 344. M. V. Shamolin, "On roughness of disspative systems and relative roughness of variable dissipation systems," the abstract of a talk at the Workshop in Vector and Tensor Analysis Named after P. K. Rashevskii, Vestn. Mosk. Univ. Ser. 1 Mat. Mekh., No. 2, 63 (2000). 345. M. V. Shamolin, "Problem of four-dimensional body motion in a resisting medium and one case of integrability," in: Book of Abstracts of the Third Int. Conf. "Differential Equations and Applications," St. Petersburg, Russia, June 1217, 2000 [in Russian], St. Petersburg State Univ., St. Petersburg (2000), p. 198. 346. M. V. Shamolin, "Comparison of some cases of integrability in dynamics of a rigid body interacting with a medium," in: Book of Abstracts of Annual Sci. Conf. GAMM 2001, ETH Zurich, 1215 February, 2001, ETH, Zurich (2001), p. 132. 347. M. V. Shamolin, "Complete integrability of equations for motion of a spatial pendulum in over-running medium flow," Vestn. Mosk. Univ. Ser. 1 Mat. Mekh., No. 5, 2228 (2001). MR1868040 (2002f:70005) 348. M. V. Shamolin, "Diagnosis problem as the main problem of general differential diagnosis problem," in: Book of Abstracts of the Third Int. Conf. "Tools for Mathematical Model ling," St. Petersburg, Russia, June 1823, 2001 [in Russian], St. Petersburg State Technical Univ., St. Petersburg (2001), p. 121. 349. M. V. Shamolin, "Integrability cases of equations for spatial dynamics of a rigid body," Prikl. Mekh., 37, No. 6, 7482 (2001). MR1872149 (2002i:70006) 350. M. V. Shamolin, "Integrability of a problem of four-dimensional rigid body in a resisting medium," the abstract of a talk at the Workshop "Actual Problems of Geometry and Mechanics," Fund. Prikl. Mat., 7, No. 1, 309 (2001). 351. M. V. Shamolin, "New integrable cases in dynamics of a four-dimensional rigid body interacting with a medium," in: Abstracts of Reports of Sci. Conf., May 2225, 2001 [in Russian], Kiev (2001), p. 344. 352. M. V. Shamolin, "New Jacobi integrable cases in dynamics of two-, three-, and fourdimensional rigid body interacting with a meduium," in: Abstracts of Reports of

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VIII Al l-Russian Congress in Theoretical and Applied Mechanics, Perm', August 2329, 2001 [in Russian], Ural Department of the Russian Academy of Sciences, Ekaterinburg (2001), pp. 599600. M. V. Shamolin, "On stability of motion of a body twisted around its longitudinal axis in a resisting medium," Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 1, 189193 (2001). M. V. Shamolin, "Pattern recognition in the model of the interaction of a rigid body with a resisting medium," in: Col. of Abstracts of First SIAM-EMS Conf. "Applied Mathematics in Our Changing World," Berlin, Germany, September 26, 2001, Springer, BirkhЁ auser (2001), p. 66. M. V. Shamolin, "Variety of types of phase portraits in dynamics of a rigid body interacting with a medium," the abstract of a talk at the Workshop "Actual Problems of Geometry and Mechanics," Fund. Prikl. Mat., 7, No. 1, 302303 (2001). M. V. Shamolin, "Dynamical systems with variable dissipation in 3D dynamics of a rigid body interacting with a medium," in: Book of Abstracts of 4th ENOC, Moscow, Russia, August 1923, 2002, Inst. Probl. Mech. Russ. Acad. Sci., Moscow (2002), p. 109. M. V. Shamolin, "Foundations in differential and topological diagnostics," in: Book of Abstracts of Annual Sci. Conf. GAMM 2002, Univ. of Augsburg, March 2528, 2002, Univ. of Augsburg (2002), p. 154. M. V. Shamolin, "Methods of analysis of dynamics of a 2D- 3D-, or 4D-rigid body with a medium," in: Abstracts, Short Communications, Poster Sessions of ICM2002, Beijing, August 2028, 2002, Higher Education Press, Beijing, China (2002), p. 268. M. V. Shamolin, "New integrable cases in dynamics of a two-, three-, and fourdimensional rigid body interacting with a medium," in: Abstracts of Reports of Int. Conf. in Differential Equations and Dynamical Systems, Suzdal', July 16, 2002 [in Russian], Vladimir State Univ., Vladimir (2002), pp. 142144. M. V. Shamolin, "On integrability of certain classes of nonconservative systems," Usp. Mat. Nauk, 57, No. 1, 169170 (2002). MR1914556 (2003g:34019) M. V. Shamolin, "Some questions of the qualitative theory of ordinary differential equations and dynamics of a rigid body interacting with a medium," J. Math. Sci., 110, No. 2, 25262555 (2002). MR1919087 (2004j:37161) M. V. Shamolin, "Foundations of differential and topological diagnostics," J. Math. Sci., 114, No. 1, 9761024 (2003). MR1965084 (2004d:93033) M. V. Shamolin, "Global structural stability in dynamics of a rigid body interacting with a medium," in: 5th ICIAM, Sydney, Australia, 711 July, 2003, Univ. of Technology, Sydney (2003), p. 306. M. V. Shamolin, "Integrability and nonintegrability in terms of transcendental functions," in: Book of Abstracts of Annual Sci. Conf. GAMM 2003, Abano TermePadua, Italy, 2428 March, 2003, Univ. of Padua (2003), p. 77. M. V. Shamolin, "Integrability in transcendental functions in rigid body dynamics," in: Abstracts of Reports of Sci. Conf. "Lomonosov Readings," Sec. Mechanics, April 1727, 2003, Moscow, M. V. Lomonosov Moscow State Univ. [in Russian], MGU, Noscow (2003), p. 130. M. V. Shamolin, "New integrable cases and families of portraits in the plane and spatial dynamics of a rigid body interacting with a medium," J. Math. Sci., 114, No. 1, 919975 (2003). MR1965083 (2004d:70008) M. V. Shamolin, "On a certain spatial problem of rigid body motion in a resisting medium," in: Abstracts of Reports of Int. Sci. Conf. "Third Polyakhov Readings," St. Petersburg, February 46, 2003 [in Russian], NIIKh St. Petersburg Univ., St.

Petersburg (2003), pp. 170171. 368. M. V. Shamolin, "On integrability of nonconservative dynamical systems in transcendental functions," in: Model ling and Study of Stability of Systems, Sci. Conf., May 2730, 2003, Abstracts of Reports [in Russian], Kiev (2003), p. 277. 369. M. V. Shamolin, "Some questions of differential and topological diagnostics," in: Book of Abstracts of 5th European Solid Mech. Conf. (ESMC-5), Thessaloniki, Greece, August 1722, 2003, Aristotle Univ. Thes. (AUT), European Mech. Sc. (EUROMECH) (2003), p. 301. 370. M. V. Shamolin, "Classes of variable dissipation systems with nonzero mean in the dynamics of a rigid body," J. Math. Sci., 122, No. 1, 28412915 (2004). MR2082898 (2005j:70014) 371. M. V. Shamolin, "Geometric representation of motion in a certain problem of body interaction with a medium," Prikl. Mekh., 40, No. 4, 137144 (2004). MR2131714 (2005m:70050) 372. M. V. Shamolin, "Integrability of nonconservative systems in elementary functions," in: X Math. Int. Conf. Named after Academician M. Kravchuk, May 1315, 2004, Kiev [in Russian], Kiev (2004), p. 279. 373. M. V. Shamolin, Methods for Analysis of Classes of Nonconservative Systems in Dynamics of a Rigid Body Interacting with a Medium [in Russian], Doctoral Dissertation, MGU, Moscow (2004). 374. M. V. Shamolin, Methods for Analysis of Classes of Nonconservative Systems in Dynamics of a Rigid Body Interacting with a Medium [in Russian], Theses of Doctoral Dissertation, MGU, Moscow (2004). 375. M. V. Shamolin, "Some cases of integrability in dynamics of a rigid body interacting with a resisting medium," in: Abstracts of Reports of Int. Conf. in Differential Equations and Dynamical Systems, Suzdal', July 510, 2004, Vladimir State Univ., Vladimir (2004), pp. 296298. 376. M. V. Shamolin, Some Problems of Differential and Topological Diagnosis [in Russian], Ekzamen, Moscow (2004). 377. M. V. Shamolin, "A case of complete integrability in spatial dynamics of a rigid body interacting with a medium taking account of rotational derivatives of force moment in angular velocity," Dokl. Ross. Akad. Nauk, 403, No. 4, 482485 (2005). MR2216035 (2006m:70012) 378. M. V. Shamolin, "Cases of complete integrability in dynamics of a four-dimensional rigid body interacting with a medium," in: Abstracts of Reports of Int. Conf. "Functional Spaces, Approximation Theory, and Nonlinear Analysis" Devoted to the 100th Anniversary of A. M. Nikol'skii, Moscow, May 2329, 2005 [in Russian], V. A. Steklov Math. Inst. of the Russian Academy of Sciences, Moscow (2005), p. 244. 379. M. V. Shamolin, "Comparison of Jacobi integrable cases of plane and spatial body motions in a medium under streamline flow-around." Prikl. Mat. Mekh., 69, No. 6, 10031010 (2005). MR2252203 (2007c:70009) 380. M. V. Shamolin, "Integrability in transcendental functions in rigid body dynamics," in: Math. Conf. "Modern Problems of Applied Mathematics and Mathematical Model ling," Voronezh, December 1217, 2005 [in Russian], Voronezh State Acad., Voronezh (2005), p. 240. 381. M. V. Shamolin, "Mathematical model of interaction of a rigid body with a resisting medium in a jet flow," in: Abstracts. Pt. 1. 76 Annual Sci. Conf. (GAMM), Luxembourg, March 28-April 1, 2005, Univ. du Luxembourg (2005), pp. 9495. 382. M. V. Shamolin, "On a certain integrable case in dynamics on so(4) в R4 ," in: Abstracts of Reports of Al l-Russian Conf. "Differential Equations and Their Applications," (SamDif-2005), Samara, June 27-July 2, 2005 [in Russian], Univers-Grupp,

Samara (2005), pp. 9798. 383. M. V. Shamolin, "On a certain integrable case of equations of dynamics in so(4) в R4 ," Usp. Mat. Nauk, 60, No. 6, 233234 (2005). MR2225204 (2007a:70009) 384. M. V. Shamolin, "On body motion in a resisting medium taking account of rotational derivatives of aerodynamic force moment in angular velocity," in: Abstracts of Reports of Sci. Conf. "Lomonosov Readings-2005," Sec. Mechanics, April, 2005, Moscow, M. V. Lomonosov Moscow State Univ. [in Russian], MGU, Moscow (2005), p. 182. 385. M. V. Shamolin, "On rigid body motion in a resisting medium taking account of rotational derivatives of areodynamical force moment in angular velocity," in: Model ling and Studying of Systems, Sci. Conf., May 2325, 2005. Abstracts of Reports [in Russian], Kiev (2005), p. 351. 386. M. V. Shamolin, "Some cases of integrability in 3D dynamics of a rigid body interacting with a medium," in: Book of Abstracts. IMA Int. Conf. "Recent Advances in Nonlinear Mechanics," Aberdeen, Scotland, August 30-September 1, 2005, Aberdeen (2005), p. 112. 387. M. V. Shamolin, "Structural stable vector fields in rigid body dynamics," in: Abstracts of 8th Conf. on Dynamical Systems (Theory and Applications) (DSTA 2005), Lodz, Poland, December 1215, 2005, Tech. Univ. Lodz (2005), p. 78. 388. M. V. Shamolin, "Structural stable vector fields in rigid body dynamics," in: Proc. of 8th Conf. on Dynamical Systems (Theory and Applications) (DSTA 2005), Lodz, Poland, December 1215, 2005, Vol. 1, Tech. Univ. Lodz (2005), pp. 429436. 389. M. V. Shamolin, "Variable dissipation dynamical systems in dynamics of a rigid body interacting with a medium," in: Differential Equations and Computer Algebra Tools, Materials of Int. Conf., Brest, October 58, 2005, Pt. 1 [in Russian], BGPU, Minsk (2005), pp. 231233. 390. M. V. Shamolin, "Almost conservative systems in dynamics of a rigid body," in: Book of Abstracts, 77th Annual Meeting of GAMM, March 2731, 2006, Technische Univ. Berlin, Technische Univ. Berlin (2006), p. 74. 391. M. V. Shamolin, "Model problem of body motion in a resisting medium taking account of dependence of resistance force on angular velocity," in: Scientifuc Report of Institute of Mechanics, Moscow State Univ. [in Russian], No. 4818, Institute of Mechanics, Moscow State Univ., Moscow (2006), p. 44. 392. M. V. Shamolin, "On a case of complete integrability in four-dimensional rigid body dynamics," Abstracts of Reports of Int. Conf. in Differential Equations and Dynamical Systems, Vladimir, July 1015, 2006 [in Russian], Vladimir State Univ., Vladimir (2006), pp. 226228. 393. M. V. Shamolin, "On tra jectories of characteristic points of a rigid body moving in a medium," in: Int. Conf. "Fifth Okunev Readings," St. Petersburg, June 26 30, 2006. Abstracts of Reports [in Russian], Balt. State Tech. Univ., St. Petersburg (2006), p. 34. 394. M. V. Shamolin, "Spatial problem on rigid body motion in a resistingmedium," in: VIII Crimeanian Int. Math. School "Lyapunov Function Method and Its Applications," Abstracts of Reports, Alushta, September 1017, 2006, Tavriya National Univ. [in Russian], DiAiPi, Simpheropol' (2006), p. 184. 395. M. V. Shamolin, "To problem on rigid body spatial drag in a resisting medium," Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, 3, 4557 (2006). 396. M. V. Shamolin, "To spatial problem of rigid body interaction with a resisting medium," in: Abstracts of Reports of IX Al l-Russian Congress in Theoretical and Applied Mechanics, Nizhnii Novgorod, August 22 28, 2006, Vol. I [in Russian], N. I. Lobachevskii Nizhegodskii State Univ., Niznii Novgorod (2006), p. 120.

397. M. V. Shamolin, "Variable dissipation systems in dynamics of a rigid body interacting with a medium," Fourth Polyakhov Readings, Abstracts of Reports of Int. Sci. Conf. in Mechanics, St. Petersburg, February 710, 2006 [in Russian], VVM, St. Petersburg (2006), p. 86. 398. M. V. Shamolin, "4D rigid body and some cases of integrability," in: Abstracts of ICIAM07, Zurich, Switzerland, June 1620, 2007, ETH, Zurich (2007), p. 311. 399. M. V. Shamolin, "A case of complete integrability in dynamics on a tangent bundle of two-dimensional sphere," Usp. Mat. Nauk, 62, No. 5, 169170 (2007). MR2373767 (2008i:37121) 400. M. V. Shamolin, "Case of complete integrability in dynamics of a four-dimensional rigid body in nonconcervative force field," in: "Nonlinear Dynamical Analysis-2007," Abstracts of Reports of Int. Congress, St. Petersburg, June 48, 2007 [in Russian], St. Petersburg State Univ., St. Petersburg (2007), p. 178. 401. M. V. Shamolin, "Cases of complete integrability in dynamics of a rigid body interacting with a medium," Abstracts of Reports of Al l-Russian Conf. "Modern Problems of Continuous Medium Mechanics" Devoted to Memory of L. I. Sedov in Connection with His 100th Anniversary, Moscow, November 1214, 2007 [in Russian], MIAN, Moscow (2007), pp. 166167. 402. M. V. Shamolin, "Cases of complete integrability in dynamics of a four-dimensional rigid body in a nonconservative force field," in: Abstract of Reports of Int. Conf. "Analysis and Singularities," Devoted to 70th Anniversary of V. I. Arnol'd, August 2024, 2007, Moscow [in Russian], MIAN, Moscow (2007), pp. 110112. 403. M. V. Shamolin, "Cases of complete integrability in elementary functions of certain classes of nonconservative dynamical systems," in: Abstracts of Reports of Int. Conf. "Classical Problems of Rigid Body Dynamics," June 913, 2007 [in Russian], Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Donetsk (2007), pp. 8182. 404. M. V. Shamolin, "Complete integrability of equations of motion for a spatial pendulum in medium flow taking account of rotational derivatives of moments of its action force," Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, 3, 187192 (2007). 405. M. V. Shamolin, "Integrability in elementary functions of variable dissipation systems," the abstract of a talk at the Workshop "Actual Problems of Geometry and Mechanics," in: Contemporary Problems in Mathematics, Fundamental Directions [in Russian], Vol. 23, All-Union Institute for Scientific and Technical Information, USSR Academy of Sciences, Moscow (2007), p. 38. 406. M. V. Shamolin, "Integrability of problem of four-dimensional rigid body motion in a resisting medium," the abstract of a talk at the Workshop "Actual Problems of Geometry and Mechanics," in: Contemporary Problems in Mathematics, Fundamental Directions [in Russian], Vol. 23, All-Union Institute for Scientific and Technical Information, USSR Academy of Sciences, Moscow (2007), p. 21. 407. M. V. Shamolin, "Integrability of strongly nonconservative systems in transcendental elementary functions," the abstract of a talk at the Workshop "Actual Problems of Geometry and Mechanics," in: Contemporary Problems in Mathematics, Fundamental Directions [in Russian], Vol. 23, All-Union Institute for Scientific and Technical Information, USSR Academy of Sciences, Moscow (2007), p. 40. 408. M. V. Shamolin, Methods of Analysis of Variable Dissipation Dynamical Systems in Rigid Body Dynamics [in Russian], Ekzamen, Moscow (2007). 409. M. V. Shamolin, "New integrable cases in dynamics of a four-dimensional rigid body interacting with a medium," the abstract of a talk at the Workshop "Actual Problems of Geometry and Mechanics," in: Contemporary Problems in Mathematics, Fundamental Directions [in Russian], Vol. 23, All-Union Institute for Scientific and

Technical Information, USSR Academy of Sciences, Moscow (2007), p. 27. 410. M. V. Shamolir, "On account of rotational derivatives of a force moment of action of the medium in angular velocity of the rigid body on body motion," the abstract of a talk at the Workshop "Actual Problems of Geometry and Mechanics," in: Contemporary Problems in Mathematics, Fundamental Directions [in Russian], Vol. 23, All-Union Institute for Scientific and Technical Information, USSR Academy of Sciences, Moscow (2007), p. 44. 411. M. V. Shamolin, "On account of rotational derivatives of aerodynamical force moment on body motion in a resisting medium," the abstract of a talk at the Workshop "Actual Problems of Geometry and Mechanics," in: Contemporary Problems in Mathematics, Fundamental Directions [in Russian], Vol. 23, All-Union Institute for Scientific and Technical Information, USSR Academy of Sciences, Moscow (2007), p. 26. 412. M. V. Shamolin, "On integrability in elementary functions of certain classes of nonconscrvative dynamical systems," in: Model ling and Study of Systems, Sci. Conf., May 2225, 2007. Abstracts of Reports [in Russian], Kiev (2007), p. 249. 413. M. V. Shamolin, "On integrability in transcendental functions," the abstract of a talk at the Workshop "Actual Problems of Geometry and Mechanics." in: Contemporary Problems in Mathematics, Fundamental Directions [in Russian], Vol. 23, All-Union Institute for Scientific and Technical Information, USSR Academy of Sciences, Moscow (2007), p. 34. 414. M. V. Shamolin, "On integrability of motion of four-dimensional body-pendulum situated in over-running medium flow," the abstract of a talk at the Workshop "Actual Problems of Geometry and Mechanics," in: Contemporary Problems in Mathematics, Fundamental Directions [in Russian], Vol. 23, All-Union Institute for Scientific and Technical Information, USSR Academy of Sciences, Moscow (2007), p. 37. 415. M. V. Shamolin, "On rigid body motion in a resisting medium taking account of rotational derivatives of aerodynamic force moment in angular velocity," the abstract of a talk at the Workshop 416. "Actual Problems of Geometry and Mechanics," in: Contemporary Problems in Mathematics, Fundamental Directions [in Russian], Vol. 23, All-Union Institute for Scientific and Technical Information, USSR Academy of Sciences, Moscow (2007), p. 44. 417. M. V. Shamolin, "On stability of a certain regime of rigid body motion in a resisting medium," in: Abstracts of Reports of Sci. Conf. "Lomonosov Readings-2007," Sec. Mechanics, Moscow, Moscow State Univ., April, 2007 [in Russian], MGU, Moscow (2007), p. 153. 418. M. V. Shamolin, "On the problem of a symmetric body motion in a resisting medium," in: Book of Abstracts of EMAC-2007 (14 July, 2007, Hobart, Australia), Univ. Tasmania, Hobart, Australia (2007), p. 25. 419. M. V. Shamolin, "On work of All-Russian Conference `Differential Equations and Their Applications,' Samara, June 27-July 2, 2005," the abstract of a talk at the Workshop "Actual Problems of Geometry and Mechanics," in: Contemporary Problems in Mathematics, Fundamental Directions [in Russian], Vol. 23, All-Union Institute for Scientific and Technical Information, USSR Academy of Sciences, Moscow (2007), p. 45. 420. M. V. Shamolin, Some Problems of Differential and Topological Diagnosis [in Russian], Ekzamen, Moscow (2007). 421. M. V. Shamolin, "The cases of complete integrability in dynamics of a rigid body interacting with a medium," in: Book of Abstracts of Int. Conf. on the Occasion

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of the 150th Birthday of A. M. Lyapunov (June 2430, 2007, Kharkiv, Ukraine), Verkin Inst. Low Temper. Physics Engineer. NASU, Kharkiv (2007), pp. 147148. M. V. Shamolin, "The cases of integrability in 2D-, 3D-, and 4D-rigid body," in: Abstracts of Short Communications and Posters of Int. Conf. "Dynamical Methods and Mathematical Model ling," Val ladolid, Spain (September 1822, 2007), ETSII, Valladolid (2007), p. 31. M. V. Shamolin, "The cases of integrability in terms of transcendental functions in dynamics of a rigid body interacting with a medium," in: Abstracts of 9th Conf. on Dynamical Systems (Theory and Applications) (DSTA 2007), Lodz, Poland, December 1720, 2007, Tech. Univ. Lodz (2007), p. 115. M. V. Shamolin, "The cases of integrability in terms of transcendental functions in dynamics of a rigid body interacting with a medium," in: Proc. of 9th Conf. on Dynamical Systems (Theory and Applications) (DSTA 2007), Lodz, Poland, December 1720, 2007, Vol. 1, Tech. Univ. Lodz (2007), pp. 415422. M. V. Shamolin, "Variety of types of phase portraits in dynamics of a rigid body interacting with a medium," the abstract of a talk at the Workshop "Actual Problems of Geometry and Mechanics," in: Contemporary Problems in Mathematics, Fundamental Directions [in Russian], Vol. 23, All-Union Institute for Scientific and Technical Information, USSR Academy of Sciences, Moscow (2007), p. 17. M. V. Shamolin, "Three-parameter family of phase portraits in dynamics of a rigid body interacting with a medium," Dokl. Ross. Akad. Nauk, 418, No. 1, 4651 (2008). MR2459491 M. V. Shamolin and D. V. Shebarshov, "Pro jections of Lagrangian tori of a biharmonic oscillator on position state and dynamics of a rigid body interacting with a medium," in: Model ling and Study of Stability of Systems, Sci. Conf., May 1923, 1997. Abstracts of Reports [in Russian], Kiev (1997), p. 142. M. V. Shamolin and D. V. Shebarshov, "Lagrange tori and the Hamilton-Jacobi equation," in: Book of Abstracts of Conf. "Partial Differential Equations: Theory and Numerical Solutions" (Praha, August 1016, 1998), Charles Univ., Praha (1998), p. 88. M. V. Shamolin and D. V. Shebarshov, "Certain problems of differential diagnosis," in: Dynamical Systems Model ling and Stability Investigation. Sci. Conf., May 2529, 1999. Abstracts of Reports (System Model ling) [in Russian], Kiev (1999), p. 61. M. V. Shamolin and D. V. Shebarshov, "Methods for solving main problem of differential diagnosis," Deposit, at VINITI, No. 1500-V99 (1999). M. V. Shamolin and D. V. Shebarshov, "Some problems of geometry in classical mechanics," Deposit, at VINITI, No. 1499-V99 (1999). M. V. Shamolin and D. V. Shebarshov, "Certain problems of differential diagnosis," the abstract of a talk at the Workshop "Actual Problems of Geometry and Mechanics," Fund. Prikl. Mat., 7, No. 1, 305 (2001). M. V. Shamolin and D. V. Shebarshov, "Certain problems of differential diagnosis," the abstract of a talk at the Workshop "Actual Problems of Geometry and Mechanics," in: Contemporary Problems in Mathematics, Fundamental Directions [in Russian], Vol. 23, All-Union Institute for Scientific and Technical Information, USSR Academy of Sciences, Moscow (2007), p. 19. M. V. Shamolin and S. V. Tsyptsyn, "Analytical and numerical study of tra jectories of body motion in a resisting medium," in: Scientific Report of Institute of Mechanics, Moscow State Univ. [in Russian], No. 4289, Institute of Mechanics, Moscow State Univ., Moscow (1993). O. P. Shorygin and N. A. Shulman, "Entry of a disk into water at an angle of attack," Uchen. Zap. TsAGI, 8, No. 1, 1221 (1977).

436. S. Smale, "Rough systems are not dense," in: A Col lection of Translations, Mathematics [in Russian], 11, No. 4, 107112 (1967). 437. S. Smale, "Differentiable dynamical systems," Usp. Mat. Nauk, 25, No. 1, 113185 (1970). MR0263116 (41 #7721) 438. V. M. Starzhinskii, Applied Methods of Nonlinear Oscil lations [in Russian], Nauka, Moscow (1977). MR0495355 (58 #14067) 439. V. A. Steklov, On Rigid Body Motion in a Fluid [in Russian], Khar'kov (1893). 440. V. V. Stepanov, A Course of Differential Equations [in Russian], Fizmatgiz, Moscow (1959). 441. V. V. Strekalov, "Reflection in entrance of a disk into a water whose plane is close to the vertical plane," Uchen. Zap. TsAGI, 8, No. 5, 6673 (1977). 442. G. K. Suslov, Theoretical Mechanics [in Russian], Gostekhizdat, Moscow (1946). 443. E. I. Suvorova and M. V. Shamolin, "Poincarґ topographical systems and come parison systems of higher orders," in: Math. Conf. "Modern Methods of Function Theory and Related Problems," Voronezh, January 26-February 2, 2003 [in Russian], Voronezh State Univ., Voronezh (2003), pp. 251252. 444. V. V. Sychev, A. I. Ruban, and G. L. Korolev, Asymptotic Theory of Separation Flows [in Russian], Nauka, Moscow (1987). 445. V. G. Tabachnikov, "Stationary characteristics of wings in small velocities under whole range of angles of attack," in: Proc. of Central Aero-Hydrodynamical Inst. [in Russian], Issue 1621, Moscow (1974), pp. 1824. 446. Ya. V. Tatarinov, Lectures on Classical Dynamics [in Russian], Izd. Mosk. Univ., Moscow (1984). MR0778381 (85m:70001) 447. V. V. Trofimov, "Embeddings of finite groups in compact Lie groups by regular elements," Dokl. Akad. Nauk SSSR, 226, No. 4, 785786 (1976). MR0439984 (55 #12865) 448. V. V. Trofimov, "Euler equations on finite-dimensional solvable Lie groups," Izv. Akad. Nauk SSSR, Ser. Mat., 44, No. 5, 11911199 (1980). MR0595263 (82e:70006) 449. V. V. Trofimov, "Symplectic structures on automorphism groups of symmetric spaces," Vestn. Mosk. Univ. Ser. 1 Mat. Mekh., No. 6, 3133 (1984). MR0775300 (86b:53038) 450. V. V. Trofimov, "Geometric invariants of completely integrable systems," in: Abstract of Reports of Al l-Union Conf. in Geometry "in the Large," Novosibirsk (1987), p. 121. 451. V. V. Trofimov and A. T. Fomenko, "A methodology for constructing Hamiltonian flows on symmetric spaces and integrability of certain hydrodynamic systems," Dokl. Akad. Nauk SSSR, 254, No. 6, 13491353 (1980). MR0592507 (82b:58038) 452. V. V. Trofimov and M. V. Shamolin, "Dissipative systems with nontrivial generalized Arnol'd-Maslov classes," the abstract of a talk at the Workshop in Vector and Tensor Analysis Named after P. K. Rashevskii, Vestn. Mosk. Univ. Ser. 1 Mat. Mekh., No. 2, 62 (2000). 453. Ch. J. de la Vallґ Poussin, Lectures on Theoretical Mechanics, Vols. I, II [Russian ee translation], Inostr. Lit., Moscow (1948, 1949). 454. L. E. Veselova, "On dynamics of a body with ellipsoidal hole filled with a fluid," Vestn. Mosk. Univ. Ser. 1 Mat. Mekh., No. 3, 6467 (1985). MR0789774 (86k:76009) 455. S. V. Vishik and S. F. Dolzhanskii, "Analogs of Euler-Poisson equations and magnetic electrodynamics related to Lie groups," Dokl. Akad. Nauk SSSR, 238, No. 5, 10321035. 456. I. N. Vrublevskaya, "On geometric equivalence of tra jectories and semitra jectories of dynamical systems," Mat. Sb., 42 (1947). 457. I. N. Vrublevskaya, "Some criteria of equivalence of tra jectories and semitra jectories

458. 459. 460. 461.

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of dynamical systems," Dokl. Akad. Nauk SSSR, 97, No. 2 (1954). MR0067480 (16,734i) C. L. Weyher, "Observations sur le vol plane par obres," L'Aeronaute (1890). E. T. Whittecker, Analytical Dynamics [Russian translation], ONTI, Moscow (1937). M. V. Yakobson, "On self-mappings of a circle," Mat. Sb., 85, 183188 (1975). N. E. Zhukovskii, "On a fall of light oblong bodies rotating around their longitudinal axis," in: A Complete Col lection of Works [in Russian], Vol. 5, Fizmatgiz, Moscow (1937), pp. 7280, 100115. N. E. Zhukovskii, "On bird soaring," in: A Complete Col lection of Works [in Russian], Vol. 5, Fizmatgiz, Moscow (1937), pp. 4959. Yu. F. Zhuravlev, "Submergence of a disk in a fluid at an angle to a free surface," in: A Col lection of Works in Hydrodynamics [in Russian], Central Aero Hydrodynamical Institute, Moscow (1959), pp. 164167. V. F. Zhuravlev and D. M. Klimov, Applied Methods in Oscil lation Theory [in Russian], Nauka, Moscow (1988). MR0987633 (90g:70001) N. A. Zlatin, A. P. Krasil'shchikov, G. I. Mishin, and N. N. Popov, Bal listic Devices and Their Applications in Experimental Studies [in Russian], Nauka, Moscow (1974).
Note: This list reflects references listed in the original paper as accurately as possible with no attempt to correct errors.

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MR2459491 70E99 37C99 37N05 Shamolin, M. V. (RS-MOSC-IMC) A three-parameter family of phase p ortraits in the dynamics of a rigid b o dy interacting with the medium. (Russian) Dokl. Akad. Nauk 418 (2008), no. 1, 4651.

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MR2432841 (2009f:70021) 70E99 70E40 70K99 Shamolin, M. V. New integrable cases in the dynamics of a b o dy interacting with a medium taking into account the dep endence of the resistance force moment on the angular velo city. (Russian. Russian summary) Prikl. Mat. Mekh. 72 (2008), no. 2, 273287; translation in J. Appl. Math. Mech. 72

(2008), no. 2, 169179. Summary (translated from the Russian): "We construct two- and three-dimensional nonlinear models of the action of a medium on a rigid body, which take into account the dependence of the arm of the force on the reduced angular velocity of the body when the moment of force is also a function of the angle of attack. We find new cases of complete integrability in elementary functions, which makes it possible to discover qualitative analogies between the motions of free bodies in a resisting medium and the oscillations of bodies that are partially fixed and immersed in a flow of the medium. We show that if the additional damping action of the medium on the body that occurs in the system is significant, then it is possible to stabilize the rectilinear translational deceleration of the body when it moves with finite angles of attack. In this connection, the question of the roughness of the description of this phenomenon is of current interest: a finer property of relative roughness is discovered in the investigation of reduced dynamical systems." c Copyright American Mathematical Society 2009, 2015

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MR2894678 70E15 70K20 Shamolin, M. V. (RS-MOSC-MC) Some mo del problems of dynamics for a rigid b o dy interacting with a medium. (English summary) Internat. Appl. Mech. 43 (2007), no. 10, 11071122.

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MR2449984 74A50 76A99 A idagulov, R. R. (RS-MOSC-IMC) ; Shamolin, M. V. (RS-MOSC-IMC) A phenomenological approach to the determination of interphase forces. (Russian) Dokl. Akad. Nauk 412 (2007), no. 1, 4447.

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MR2373767 (2008i:37121) 37J35 34C20 70E40 70H06 Shamolin, M. V. (RS-MOSC) A case of complete integrability in the dynamics on the tangent bundle of a two-dimensional sphere. (Russian) Uspekhi Mat. Nauk 62 (2007), no. 5(377), 169170; translation in Russian Math. Surveys 62 (2007), no. 5, 10091011.

From the text (translated from the Russian): "We propose a new approach that enables us to obtain integrable cases in the dynamics of a free rigid body, namely, to integrate dynamic equations on the space R3 в so(3), in a nonconservative (dissipative) force field."
References

1. M. B. Phys. 2. M. B. Phys. 3. M. B. Math.

..., .... PAH 364:5 (1999), 627629; English transl., M. V. Shamolin, Dokl. 44:2 (1999), 110113. MR1702618 (2000k:70008) ..., .... PAH 371:4 (2000), 480483; English transl., M. V. Shamolin, Dokl. 45:4 (2000), 171174. MR1776307 (2001k:70006) ..., YMH 54:5 (1999), 181182; English transl., M. V. Shamolin, Russian Surveys 54:5 (1999), 10421043. MR1741681 (2000j:37021)
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MR2342525 (2008i:58003) 58A05 18A99 57R99 A idagulov, R. R. (RS-MOSCM) ; Shamolin, M. V. (RS-MOSCM) Manifolds of continuous structures. (Russian. Russian summary) Sovrem. Mat. Fundam. Napravl. 23 (2007), 7186; translation in J. Math. Sci. (N. Y.) 154 (2008), no. 4, 523538.

Summary (translated from the Russian): "In modern mathematics, the theory of categories and functors provides a language for describing arbitrary sets. Its main distinguishing feature is that instead of considering an individual set with some given structure, one considers all identically structured sets simultaneously. In this paper, we describe systems by categories. The system itself is a category that consists of a class of ob jects and a class of morphisms. The axiomatics of the mathematical structure defining the category distinguishes the given system from among other systems, and the ob jects of the category model the state of systems."
References

1. P. S. Aleksandrov, Combinatorial Topology [in Russian], Moscow-Leningrad (1947). MR0025723 (10,55b) 2. P. S. Aleksandrov, Introduction to the General Theory of Sets and Functions [in Russian], Moscow-Leningrad (1948). 3. P. S. Aleksandrov and B. A. Pasynkov Introduction to the Theory of Dimension. Introduction to the Theory of Topological Spaces and General Theory of Dimension [in Russian], Moscow (1973). 4. P. S. Aleksandrov, Introduction to the Homological Theory of Dimension and General Combinatorial Topology [in Russian], Moscow (1975). 5. A. V. Arkhangel skii asnd V. I. Ponomarev, Foundations of General Topology in Problems and Exercises [in Russian], Moscow (1974). 6. I. Bukur and A. Delyanu, Introduction to the Theory of Categories and Functors [Russian translation] (1972). 7. N. Bourbaki, General Topology. Basic Structures [Russian translation], Moscow (1968). MR0244925 (39 #6238) 8. N. Bourbaki, General Topology. Topological Groups. Numbers and Groups and Spaces Related to Them [Russian translation], Moscow (1969). MR0256328 (41 #984) 9. N. Bourbaki, General Topology. The Use of Real Numbers in General Topology. Functional Spaces. Summary of Results. Dictionary [Russian translation], Moscow (1975). 10. H. Weyl, Mathematical Way of Thinking [Russian translation], Nauka, Moscow (1989). MR1085250 (92e:01081) 11. R. Goldblatt, Toposes. A Categorial Analysis of Logics [Russian translation], Mir, Moscow (1973). 12. V. K. Zakharov and A. V. Mikhalev, "A local theory of classes and sets as a foundation for the theory of categories," in: Mathematical Methods and Applications. Proceedings of the Ninth Mathematical Studies. Moscow State Construction University [in Russian], Mosk. Gos. Stroit. Univ., Moscow (2002), pp. 9194. 13. M. Kashivara and P. Shapira, Sheafs on Manifolds [Russian translation], Mir, Moscow (1997). 14. G. Kelly, General Topology [Russian translation], Nauka, Moscow (1968). 15. B. P. Komrakov, Structures on Manifolds and Homogeneous Spaces [in Russian], Nauka Tekhnika, Minsk (1978). MR0519337 (80h:53001) 16. P. Cohn, Universal Algebra [Russian translation], Mir, Moscow (1968). MR0258711 (41 #3357)

17. K. Kuratowsky, Topology. Vols. 12 [Russian translation], Moscow (19661969). 18. A. P. Levich, Theory of Sets, the Language of the Theory of Categories and Their Application in Theoretical Biology [in Russian], Izd. Mosk. Gos. Univ., Moscow (1982). 19. S. Leng, Introduction to the Theory of Differentiable Manifolds [Russian translation], Moscow (1967). 20. S. Macleyn, Categories for Working Mathematicians [Russian translation], Fizmatlit, Moscow (2004). 21. G. Milnor and A. Walles, Differential Topology. Beginner's Course [Russian translation], Moscow (1972). 22. Nestruev, Jet. Smooth Manifolds and Observables [in Russian], MTsNMO, Moscow (2000). 23. A. S. Parkhomenko, What is a Line [in Russian], Moscow (1954). 24. L. S. Pontryagin, Foundations of Combinatorial Topology [in Russian], MoscowLeningrad (1947). MR0033516 (11,450e) 25. L. S. Pontryagin, Continuous Groups [in Russian], Moscow (1973). 26. M. M. Postnikov, Introduction to Morse Theory [in Russian], Moscow (1971). MR0315739 (47 #4288) 27. E. Spenier, Algebraic Topology [Russian translation], Moscow (1971). 28. N. Steenrode, W. Chinn, Initial Concepts of Topology [Russian translation], Moscow (1967). 29. A. Frelicher and V. Bucher, Differential Calculus in Vector Spaces without Norm [Russian translation], Mir, Moscow (1970). MR0352977 (50 #5463) 30. S. Helgason, Differential Geometry and Symmetrical Spaces [Russian translation], Mir, Moscow (1964). 31. M. Sh. Tsalenko and E. G, Shulgeifer, Foundations of the Theory of Categories [in Russian], Nauka, Moscow (1974). MR0374225 (51 #10425) 32. H. Hasse, Hohere Algebra I, II, Sammlung Goschen (1926). 33. S. Lefschetz, Topologie, Amer. Math. Soc., New York (1930). 34. Steinitz, Algebraische Theorieder Korper, initially published in Krell magazine, 1910 and then published by R. Basr and H. Hasse in V. de Gruyter's Publisher's House (1930). 35. B. Van der Waerden, Modern Algebra I, II, Springer-Verlag (1930). 36. O. Veblen, Analysis Situs, Amer. Math. Soc., New York (1931). 37. H. Weyl, Die Ideeder Riemannschen Flache, Teubner (1923).
Note: This list reflects references listed in the original paper as accurately as possible with no attempt to correct errors.

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MR2342524 (2009g:74015) 74B05 35Q72 A idagulov, R. R. (RS-MOSCM) ; Shamolin, M. V. (RS-MOSCM) A general sp ectral approach to the dynamics of a continuous medium. (Russian. Russian summary) Sovrem. Mat. Fundam. Napravl. 23 (2007), 5270; translation in J. Math. Sci. (N. Y.) 154 (2008), no. 4, 502522.

In this paper the authors come to the conclusion that the system of conservation mass and moment is not suitable for the calculation of resonances and instabilities in a medium. In the opinion of the authors, the homogenization method is also not useful in such problems. A system of pseudo-differential equations with more precise dispersion relations in a medium is obtained by varying the waves and amplitudes description of the medium. In accord with this method the authors give a pseudo-differential system for rarefied gas dynamic, for a pseudo-differential version of Hooke's law, and discuss the possibility of definition of the medium by means of spectral properties of the medium. Mikhail P. Vishnevskii
References

1. G. Bird, Molecular Gas Dynamics [Russian translation], Mir, Moscow (1981). 2. I. M. Gel fand and G. E. Shilov, Generalized Functions and Operations on Them [in Russian], Fizmatlit, Moscow (1959). 3. Yu. V. Egorov and M. A. Shubin, "Linear partial differential equations. Elements of modern theory," Itogi Nauki Tekh. Sovr. Probl. Mat. Fundam. Napravl., VINITI, Moscow (1988), 31, pp. 5125. MR1175406 (93e:35001) 4. D. N. Zubarev, V. G. Morozov, and G. Repke, Statistical Mechanics of Disequilibrium States [in Russian], Fizmatlit, Moscow (2002). 5. A. G. Kulikovskii and E. N. Sveshnikova, Nonlinear Waves in Elastic Media [in Russian], Moskovskii Litsei, Moscow (1998). 6. A. A. Lokshin and Yu. V. Suvorova, Mathematical Theory of Wave Propagation in Media with Memory [in Russian], Moscow State Univ., Moscow (1982). MR0676810 (84m:73031) 7. V. Yu. Lyapidevskii and V. M. Teshukov, Mathematical Models of Propagation of Long Waves in an Inhomogeneous Fluid [in Russian], Novosibirsk (2000). 8. V. P. Maslov, Operator Methods [in Russian], Nauka, Moscow (1973). MR0445305 (56 #3647) 9. S. Mizohato, Theory of Partial Differential Equations [Russian translation], Mir, Moscow (1977). 10. R. I. Nigmatulin, Foundations of Mechanics of Heterogeneous Media [in Russian], Nauka, Moscow (1978). MR0518814 (80b:76040) 11. V. N. Nikolaevskii, Geomechanics and Fluid Dynamics [in Russian], Nedra, Moscow (1996). 12. P. Reziboi and M. de Lener, Classical Kinetic Theory of Fluids and Gases [Russian translation], Mir, Moscow (1980). 13. V. Ya. Rudyak, Statistical Theory of Dissipative Processes in Gases and Fluids [in Russian], Nauka, Novosibirsk (1987). 14. L. I. Sedov, Mechanics of Continua, [in Russian], Nauka, Moscow (1970). MR0413651 (54 #1765) 15. Hewitt and Ross, Abstract Harmonic Analysis, Vol. 2 [Russian translation], Mir, Moscow (1975). MR0396828 (53 #688) 16. G. Grubb, Functional Calculus of Pseudo-Differential Boundary Problems, BirkhЁ auser (1986). MR0885088 (88f:35002)

Note: This list reflects references listed in the original paper as accurately as possible with no attempt to correct errors.

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MR2342523 (2008h:22005) 22A30 A idagulov, R. R. (RS-MOSCM) ; Shamolin, M. V. (RS-MOSCM) Archimedean uniform structures. (Russian. Russian summary) Sovrem. Mat. Fundam. Napravl. 23 (2007), 4651; translation in J. Math. Sci. (N. Y.) 154 (2008), no. 4, 496501.

Summary (translated from the Russian): "In mathematics, the concept of the Archimedean property is used in connection with two different ob jects: orderings of groups and valuations of rings. In both cases, one can define a topology on these objects and even a uniform structure; in the first case, an interval topology, and in the second, a certain valuation. It turns out that these two uses of the term Archimedean property and the somewhat regrettable term `topological group without small subgroups' are special cases of the concept of the Archimedean property of a topological group."
References

1. P. S. Aleksandrov, Combinatorial Topology [in Russian], MoscowLeningrad (1947). MR0025723 (10,55b) 2. P. S. Aleksandrov, Introduction to the General Theory of Sets and Functions [in Russian], MoscowLeningrad (1948). 3. P. S. Aleksandrov and B. A. Pasynkov, Introduction to the Dimensionality theory. Introduction to the Theory of Topological Spaces and General Dimensionality Theory [in Russian], Moscow (1973). 4. P. S. Aleksandrov, Introduction to the Homological Dimensionality Theory and General Combinatorial Topology [in Russian], Moscow (1975). MR0515285 (58 #24234a) 5. M. Atiyah and I. Macdonald, Introduction to Commutative Algebra. 6. N. Bourbaki General Topology. Topological Groups. Numbers and Groups and Spaces Related to Them [Russian translation], Nauka, Moscow (1969). MR0256328 (41 #984) 7. N. Bourbaki, Commutative Algebra [Russian translation], Nauka, Moscow (1971). 8. O. Zarissky and P. Samuel, Commutative Algebra. 9. I. Kaplansky, Lie Algebras and Local ly Compact Groups [Russian translation], Mir, Moscow (1974). 10. G. Kelly General Topology [Russian translation], Nauka, Moscow (1968). 11. B. P. Komrakov, Structures on Manifolds and Homogeneous Spaces [in Russian], Minsk (1978). MR0519337 (80h:53001) 12. P. Cohn, Universal Algebra [Russian], Mir, Moscow (1968). MR0258711 (41 #3357) 13. K. Kuratowsky, Topology, Vols. 12, [Russian translation], Moscow (19661969). 14. S. Lang, Introduction to the Theory of Differential Manifolds [Russian translation], Moscow (1967).

15. G. Milnor and A. Walles, Differential Topology. Initial Course [Russian translation], Moscow (1972). 16. L. S. Pontryagin, Foundations of Combinatorial Topology [in Russian], Moscow Leningrad (1947). MR0033516 (11,450e) 17. L. S. Pontryagin, Continuous Groups [in Russian], Moscow (1973). 18. E. Spenier, Algebraic Topology [Russian translation], Moscow (1971). 19. N. Stinrode and W. Chinn, Initial Concepts of Topology [Russian translation], Moscow (1967). 20. A. FrЁ her and V. Bucher, Differential Calculus in Vector Spaces without Norm olic [Russian translation], Mir, Moscow (1970). MR0352977 (50 #5463) 21. S. Helgason, Differential Geometry and Symmetric Spaces [Russian translation], Mir, Moscow (1964). 22. H. Hasse, Hohere Algebra I, II, Sammlung Goschen (1926). 23. S. Lefschetz, Topologie, Amer. Math. Soc., New York (1930). 24. B. Van der Waerden, Moderne Algebra I, II, Springer-Verlag (1930). MR0002841 (2,120b) 25. O. Veblen, Analysis Situs, Amer. Math. Soc. New York (1931). 26. H. Weyl, Die IdeederRiemannschen Flache, Teubner (1923).
Note: This list reflects references listed in the original paper as accurately as possible with no attempt to correct errors.

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MR2342521 01A70 Georgievski D. V. ; Shamolin, M. V. i, Valeri Vladimirovich Trofimov. (Russian) i Sovrem. Mat. Fundam. Napravl. 23 (2007), 515; translation in J. Math. Sci. (N. Y.) 154 (2008), no. 4, 449461.

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Note: This list reflects references listed in the original paper as accurately as possible with no attempt to correct errors.

c Copyright American Mathematical Society 2015

Citations From References: 3 From Reviews: 0

MR2252203 (2007c:70009) 70E15 70E40 70E45 70H06 Shamolin, M. V. Comparison of Jacobi-integrable cases of two- and three-dimensional motions of a b o dy in a medium in the case of a jet flow. (Russian. Russian summary) Prikl. Mat. Mekh. 69 (2005), no. 6, 10031010; translation in J. Appl. Math. Mech. 69

(2005), no. 6, 900906 (2006). Summary (translated from the Russian): "We show the complete integrability of the plane problem of the motion of a rigid body in a resisting medium under jet flow conditions, when one first integral, which is a transcendental function of quasi-velocities (in the sense of the theory of functions of a complex variable with essentially singular points), exists in the system of equations of motion. It is assumed that the entire interaction of the medium with the body is concentrated on a part of the surface of the

body that has the shape of a (one-dimensional) plate. We generalize this plane problem to the three-dimensional case, where a complete set of first integrals exists for the equations of motion: one analytic, one meromorphic, and one transcendental. Here we assume that the entire interaction of the medium with the body is concentrated on part of the surface of the body that has the shape of a flat (two-dimensional) disk. We also attempt to construct a generalization of the `low-dimensional' cases to the dynamics of a so-called four-dimensional rigid body whose interaction with a medium is concentrated on a part of the (three-dimensional) surface of the body that has the shape of a (threedimensional) sphere. In this case, the angular velocity vector is six-dimensional, while the velocity of the center of mass is four-dimensional." c Copyright American Mathematical Society 2007, 2015

Citations From References: 6 From Reviews: 0

MR2225204 (2007a:70009) 70E40 37J35 70H06 Shamolin, M. V. (RS-MOSC) On an integrable case of equations of dynamics on so(4) в R4 . (Russian) Uspekhi Mat. Nauk 60 (2005), no. 6(366), 233234; translation in Russian Math. Surveys 60 (2005), no. 6, 12451246.

The four-dimensional analog of the problem on the motion action of resistance forces with variable dissipation and of a The rotational part of the equations of motion is considered the body is dynamically symmetric. It is shown that under equations of motion possess an invariant surface. For the surface transcendental first integrals are indicated.
References

of a rigid body under the servo-constraint is studied. under the assumption that appropriate conditions the motions restricted to this Alexander Burov

1. O. I. Bogoyavlenskii, Dokl. Akad. Nauk SSSR 287 (1986), 11051108; English transl., Soviet Phys. Dokl. 31 (1986), 309311. MR0839710 (87j:70005) 2. O. I. Bogoyavlenskii and G. F. Ivakh, Uspekhi Mat. Nauk 40:4 (1985), 145146; English transl., Russian Math. Surveys 40:4 (1985), 161162. MR0807729 (87g:58035) 3. M. V. Shamolin, J. Math. Sci. (New York) 114 (2003), 919975. MR1965083 (2004d:70008) 4. M. V. Shamolin, Dokl. Akad. Nauk 375 (2000), 343346; English transl., Dokl. Phys. 45:11 (2000), 632634. MR1833828 (2002c:70005) 5. V. V. Trofimov and A. T. Fomenko, Itogi Nauki i Tekhniki: Sovremennye Problemy Mat.: Fundamental'nye Napravleniya, vol. 29, VINITI, Moscow 1987, pp. 3108; English transl., J. Soviet Math. 39 (1987), 26832746. MR0892743 (88i:58059) 6. S. A. Chaplygin, Selected works, Nauka, Moscow 1976. (Russian) MR0424502 (54 #12464) 7. M. V. Shamolin, Dokl. Akad. Nauk 364 (1999), 627629; English transl., Dokl. Phys. 44:2 (1999), 110113. MR1702618 (2000k:70008)

Note: This list reflects references listed in the original paper as accurately as possible with no attempt to correct errors.

c Copyright American Mathematical Society 2007, 2015

Citations From References: 3 From Reviews: 0

MR2216035 (2006m:70012) 70E40 Shamolin, M. V. (RS-MOSC-IMC) A case of complete integrability in the three-dimensional dynamics of a rigid b o dy interacting with a medium taking into account the rotational derivatives of the momentum of forces of angular velo city. (Russian) Dokl. Akad. Nauk 403 (2005), no. 4, 482485; translation in Dokl. Phys. 50 (2005), no.

8, 414418. From the text (translated from the Russian): "Because of its complexity, the problem of the motion of a rigid body in an unbounded medium requires the introduction of simplifying restrictions. The main goal is to introduce hypotheses that allow one to study the motion of a rigid body separately from the motion of the medium in which the body is located. On the one hand, a similar approach was taken in the classical Kirchhoff problem of the motion of a body in an unbounded ideal incompressible fluid which is at rest at infinity and which undergoes irrotational motion. On the other hand, it is clear that the aforementioned Kirchhoff problem does not exhaust the possibilities of this type of modeling. "In this paper, we consider the possibility of transferring the results of the dynamics of the plane-parallel motion of a homogeneous axisymmetric rigid body interacting at its front circular face with a uniform flow of a resisting medium to the case of threedimensional motion. Here, unlike in previous papers on the modeling of the interaction between a medium and a rigid body, we take into account the effects of the so-called rotational derivatives of the moment of hydroaerodynamic forces with respect to the components of the angular velocity of the rigid body itself." c Copyright American Mathematical Society 2006, 2015

Citations From References: 1 From Reviews: 0

MR1806854 90B25 Borisenok, I. T. ; Shamolin, M. V. (RS-MOSC) Solution of a problem of differential diagnostics. (Russian. English, Russian summaries)

New computer technologies in control systems (Russian) (Pereslavl -Zalesski 1996). i, Fundam. Prikl. Mat. 5 (1999), no. 3, 775790. This item will not be reviewed individually. {For the entire collection see MR1806845 (2001g:49003)} c Copyright American Mathematical Society 2015

Citations From References: 5 From Reviews: 0

MR1741681 (2000j:37021) 37C20 34D30 70E99 70K99 Shamolin, M. V. (RS-MOSC) Robustness of dissipative systems and relative robustness and nonrobustness of systems with variable dissipation. (Russian) Uspekhi Mat. Nauk 54 (1999), no. 5(329), 181182; translation in Russian Math. Surveys 54 (1999), no. 5, 10421043.

From the text (translated from the Russian): "We present a brief survey of problems of relative structural stability (relative robustness) of dynamical systems considered not on the entire space of dynamical systems but only on some subspace of it [M. V. Shamolin, Uspekhi Mat. Nauk 51 (1996), no. 1(307), 175176; MR1392692 (97f:70010)]." c Copyright American Mathematical Society 2000, 2015

Citations From References: 12 From Reviews: 0

MR1702618 (2000k:70008) 70E40 70H06 Shamolin, M. V. (RS-MOSC-MC) New integrable, in the sense of Jacobi, cases in the dynamics of a rigid b o dy interacting with a medium. (Russian) Dokl. Akad. Nauk 364 (1999), no. 5, 627629; translation in Dokl. Phys. 44 (1999), no.

2, 110113. From the text (translated from the Russian): "The dynamic model of the interaction of a rigid body with a resisting medium under jet flow conditions that is considered not only allows us to successfully transfer the results of corresponding problems from the two-dimensional dynamics of a rigid body interacting with a medium and to obtain

their three-dimensional analogues, it also reveals new Jacobi-integrable cases. Here the integrals can sometimes be expressed in terms of elementary functions. We demonstrate the integrability of the classical problem of a spherical pendulum submerged in an incident flow of a medium and the problem of the three-dimensional motion of a body in the presence of a servoconstraint. We also give mechanical and topological analogues of the latter two problems." c Copyright American Mathematical Society 2000, 2015

Citations From References: 9 From Reviews: 0

MR1657632 (99h:34006) 34A20 30D30 Shamolin, M. V. (RS-MOSC) On integrability in transcendental functions. (Russian) Uspekhi Mat. Nauk 53 (1998), no. 3(321), 209210; translation in Russian Math. Surveys 53 (1998), no. 3, 637638.

The problem of integrability of systems of ordinary differential equations in transcendental functions is discussed in this paper. Shamil Makhmutov c Copyright American Mathematical Society 1999, 2015

Citations From References: 7 From Reviews: 0

MR1479402 (99a:34089) 34C05 34C11 Shamolin, M. V. (RS-MOSC) Spatial Poincarґ top ographical systems and comparison systems. (Russian) e Uspekhi Mat. Nauk 52 (1997), no. 3(315), 177178; translation in Russian Math. Surveys 52 (1997), no. 3, 621622.

The notions of the Poincarґ topographical system, the characteristic function and the e comparison system are generalised for the higher-dimensional case. Theorem. Assume that in the 1-connected domain D Rn containing a unique singular point x0 of the smooth vector field v , there exists the hypersurface x0 , D = such that there exists a Poincarґ topographical system, having a center at x0 and defined by a e smooth function V , extended along up to , filling the domain K D and such that (v , grad V )|Rn 0 in K . Then in the domain D there is no closed curve consisting of the tra jectories of the vector field v and intersecting . Applications to the center-focus problem are discussed. Natalia Borisovna Medvedeva c Copyright American Mathematical Society 1999, 2015

Citations From References: 6 From Reviews: 0

MR1644665 (99e:70027) 70E99 34C99 Shamolin, M. V. An intro duction to the problem of the braking of a b o dy in a resisting medium, and a new two-parameter family of phase p ortraits. (Russian. Russian summary) Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1996, no. 4, 5769, 112.

Summary (translated from the Russian): "We actually begin with a consideration of a model version of the problem of free plane-parallel braking of a rigid body in a resisting medium under conditions of jet-type or detached flow. We carry out a qualitative analysis of the systems of differential equations that describe a given class of motions and, based on it, obtain a new two-parameter family of phase portraits consisting of an uncountable set of nonequivalent portraits without limit cycles." c Copyright American Mathematical Society 1999, 2015

Citations From References: 6 From Reviews: 0

MR1440994 (98b:70009) 70E15 34C05 70K05 76B10 Shamolin, M. V. (RS-MOSC) Manifold of phase p ortrait typ es in the dynamics of a rigid b o dy interacting with a resisting medium. (Russian) Dokl. Akad. Nauk 349 (1996), no. 2, 193197; translation in Phys. Dokl. 41 (1996), no.

7, 320324. The author considers a version of the plane-parallel motion of a rigid body in a resisting medium. He assumes that a part of the body's surface has the shape of a flat plate and that the interaction of the medium with the body is concentrated at precisely this part. A similar model proves useful in the investigation of bodies moving in a jet flow. By eliminating the cyclic coordinates, the equations of motion are reduced to a secondorder autonomous system. The author uses qualitative methods to study and classify the phase tra jectories of the reduced dynamical system. In particular, he studies limit cycles and singular points of the vector field, and the behavior of stable and unstable separatrices. The presence of free parameters adds additional complexity to the system. For example, the author presents a two-parameter family of dynamical systems with a countable set of topologically different phase portraits. Igor Gashenenko c Copyright American Mathematical Society 1998, 2015

Citations From References: 5 From Reviews: 1

MR1392692 (97f:70010) 70E15 Shamolin, M. V. (RS-MOSC) Determination of relative robustness and a two-parameter family of phase p ortraits in the dynamics of a rigid b o dy. (Russian) Uspekhi Mat. Nauk 51 (1996), no. 1(307), 175176; translation in Russian Math. Surveys 51 (1996), no. 1, 165166.

The author gives a definition of the relative robustness of a system of differential equations that differs from previously used definitions. It contains two main points: sufficient smallness of the homeomorphism that produces the equivalence, and C 1 topology in the space of vector fields. As an example, the author considers a problem that describes the dynamics of a rigid body interacting with a medium. He proves a theorem on absolute robustness, from which it follows that there exists a two-parameter family of phase portraits in which a degenerate transition occurs in the passage from one topological portrait type to another. It should be noted that the space in which the system is absolutely robust has finite measure, while the space in which the system is a system of the first degree of robustness has measure zero in the original space. Gennady Victorovich Gorr c Copyright American Mathematical Society 1997, 2015

Citations From References: 4 From Reviews: 0

MR1809236 70K99 34D30 37C20 37N05 Shamolin, M. V. Relative structural stability of dynamical systems in the problem of the motion of a b o dy in a medium. (Russian)

Analytic, numerical and experimental methods in mechanics (Russian), 1419, Moskov. Gos. Univ., Moscow, 1995. This item will not be reviewed individually. {For the entire collection see MR1809235 (2001g:00013)} c Copyright American Mathematical Society 2015

Citations From References: 7 From Reviews: 0

MR1298329 (95g:70006) 70E15 34C99 70K05 Shamolin, M. V. (RS-MOSC) A new two-parameter family of phase p ortraits in the problem of the motion of a b o dy in a medium. (Russian) Dokl. Akad. Nauk 337 (1994), no. 5, 611614; translation in Phys. Dokl. 39 (1994), no.

8, 587590. The paper deals with the Kirchhoff problem on the motion of a rigid body in an infinite ideal incompressible fluid medium. The author considers a sixth order dynamic system from which a second order subsystem splits off. The complete topological classification of phase portraits is carried out and a two-parameter family of phase portraits consisting of an uncountable set of topologically distinct phase portraits is isolated. V. A. Sobolev c Copyright American Mathematical Society 1995, 2015

Citations From References: 6 From Reviews: 0

MR1293942 (95e:34036) 34C35 34C99 Shamolin, M. V. Existence and uniqueness of tra jectories that have p oints at infinity as limit sets for dynamical systems on the plane. (Russian. Russian summary) Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1993, no. 1, 6871, 112.

Summary (translated from the Russian): "We consider dynamical systems on the plane, cylinder and sphere. For some classes of systems we prove the existence and uniqueness of tra jectories going out to infinity in the plane. For one-parameter systems of equations having monotonicity properties on two-dimensional oriented surfaces, we examine the problem of the existence and uniqueness of limit sets and their monotone dependence on the parameters." c Copyright American Mathematical Society 1995, 2015

Citations From References: 7 From Reviews: 0

MR1258007 (94i:70027) 70K99 34C99 70K20 76B05 Shamolin, M. V. Phase p ortrait classification in a problem on the motion of a b o dy in a resisting medium in the presence of a linear damping moment. (Russian. Russian summary) Prikl. Mat. Mekh. 57 (1993), no. 4, 4049; translation in J. Appl. Math. Mech. 57

(1993), no. 4, 623632. Summary (translated from the Russian): "We present a qualitative analysis of a dynamical system that describes a model version of the problem of the plane-parallel motion

of a body in a medium with jet or separated flow when the entire interaction of the medium with the body is concentrated on a part of the surface of the body having the form of a flat plate. The force of the interaction is directed along the normal to the plate, and the point of application of this force depends only on the angle of attack. A thrust force acts along the mean perpendicular to the plate, which ensures that the value of the velocity of the center of the plate remains constant throughout the motion. In addition, a damping moment, linear with respect to the angular velocity, is imposed on the body. We carry out the phase portrait classification of the system depending on the coefficient of the moment. We note the mechanical and topological analogies with a pendulum fixed in a flowing medium." c Copyright American Mathematical Society 1994, 2015

Citations From References: 6 From Reviews: 0

MR1223987 (94b:34060) 34C99 34C05 34C25 76D99 Shamolin, M. V. Application of the metho ds of Poincarґ top ographical systems and comparison e systems in some concrete systems of differential equations. (Russian. Russian summary) Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1993, no. 2, 6670, 113.

Summary (translated from the Russian): "We consider autonomous systems on the plane or a two-dimensional cylinder and study questions of the existence for various classes of systems of Poincarґ topographical systems or more general comparative systems. As e applications we consider dynamical systems that describe the plane-parallel motion of a body in a resisting medium as well as various model variants of it." c Copyright American Mathematical Society 1994, 2015

Citations From References: 6 From Reviews: 0

MR1293705 (95d:34060) 34C23 34C05 34C25 70E15 Shamolin, M. V. Closed tra jectories of various top ological typ es in the problem of the motion of a b o dy in a resisting medium. (Russian. Russian summary) Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1992, no. 2, 5256, 112.

Summary (translated from the Russian): "We consider dynamical systems on a twodimensional cylinder. We sharpen the theorems of Hopf, Bendixson and Dulac, after which it becomes possible to study closed tra jectories of various topological types in connection with the problem of the motion of a body in a resisting medium. We give an example of a class of systems in the phase space of which there exists a continuum of

closed tra jectories of different types." c Copyright American Mathematical Society 1995, 2015

Citations From References: 6 From Reviews: 0

MR1214592 (93k:70028) 70H05 34C05 34C25 58F40 70E15 Shamolin, M. V. On the problem of the motion of a b o dy in a resistant medium. (Russian. Russian summary) Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1992, no. 1, 5258, 112.

Summary (translated from the Russian): "We continue a qualitative analysis of a model variant of the interaction of a body with a resistant medium. Under the assumption that the motion is plane-parallel we completely analyze the case of constant velocity of the center of mass. We prove the presence of nonisolated periodic solutions, the absence of limit cycles and transcendental integrability, and present necessary and sufficient conditions for expressing the integral in terms of elementary functions." c Copyright American Mathematical Society 1993, 2015

Citations From References: 10 From Reviews: 1

MR1029730 (90k:70007) 70E99 58F40 76D25 Samsonov, V. A. [Samsonov, Vitaly A.] ; Shamolin, M. V. On the problem of the motion of a b o dy in a resisting medium. (Russian) Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1989, no. 3, 5154, 105.

Summary (translated from the Russian): "We consider a variant of the problem on the motion of a body in a resisting medium under the assumption that the interaction of the medium with the body is confined to a part of the surface of the body, which has the form of a flat plate. For plane-parallel motion we completely analyze the case of constant velocity of the center of the plate. We prove the nonexistence of auto-oscillations and prove transcendental integrability." c Copyright American Mathematical Society 1990, 2015