Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://www.kiam1.rssi.ru/pubs/prep_2013_046.pdf Äàòà èçìåíåíèÿ: Tue Oct 8 14:40:35 2013 Äàòà èíäåêñèðîâàíèÿ: Thu Feb 27 19:55:53 2014 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: ð ï ð ï ð ï ð ï ð ï ð ï ð ï ð ï ð ï ð ï ð ï ð ï ð ï ð ï ð ï

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ABSTRACT This work concerns the orbit choice problem in case of the Millimetron mission ­ the deployment of a space telescope on some qua si-periodic trajectory in the vicinity of the Sun-Earth system L2 point. The classification of the periodic motions in the vicinity of the collinear libration points is presented along with the pioneer libration point missions' overview. The periodic solutions of the restricted three body problem, which have been suggested by other authors as the prototypes of the Millimetron orbit are presented. These periodic solutions have been simulated with the help of dynamical model which takes into account all major forces affecting spacecraft. The final part of this preprint contains appropriate halo orbits with given geometrical dimensions such as 1 million km z-component amplitude. These orbits are regarded by the author as the most convenient ones for the Millime tron spacecraft deployment. One of these halo-orbits has been chosen as the nominal trajectory for the Millimetron mission. These orbits are quasi periodic and require station-keeping impulses once every 70-90 days. The calculation algorithms providing such halo orbits with the low-energy transfer trajectories have been described in previous publications. Key words: halo orbits, L2 point, Millimetron.


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1. .. . . // . 2005. . 43. 2 . 88-110. 2. .. . // . 2009. . 47. 1 . 64-78.


20 3. .. . // . 2009. . 47. 5 . 444-451. 4. .. "" . // . 2010. . 48. 3. . 271-278 5. .. L1 L2 .// . 2011. . 49. 4. . 335-344. 6. .. . 2. 1/1. // . 2012. . 50. 1. .68-78. 7. .. . URL: http://www.asc.rssi.ru/millimetron/millim.htm 8. .., .., .., .., .., .., .., .. L2 -. // . .. , 2013, 6. URL: http://keldysh.ru/papers/2013/prep2013_6.pdf 9. .., .., .. L2 ­ // . .. , 2012, 66. URL: http://keldysh.ru/papers/2012/prep2012_66.pdf 10. .., .., .. L2 ­ // . .. , 2012, 65. URL: http://keldysh.ru/papers/2012/prep2012_65.pdf 11. Farquhar R.W. The Control and Use of Libration-Point Satellites // Ph.D. Dissertation, Dept. of Aeronautics and Astronautics, Stanford University, Stanford, CA, 1968 12. Canalias E., Gomez G., Marcote M., Masdemont J.J. Assessment of Mission Design Including Utilization of Libration Points and Weak Stability Boundaries. ­ Department de Matematica Aplicada, Universitat Politecnica de Catalunya and Department de Matematica Aplicada, Universitat de Barcellona. 13. Richardson D.L. A note on the Lagrangian Formulation for Motion about the Collinear Points. // Celestial Mechanics, 22(3):231­235, 1980. 14. .., .., .., .. . ­ .: , 1966 ., 568 . 15. Jorba þ., Villanueva J. On the Persistence of Lower Dimensional Invariant Tori Under Quasiperiodic Perturbations. // J. Nonlinear Science, 7:427­473, 1997. 16. .. . ­ .: , 1978.


21 17. . . ­ -: , 2004. 18. .., .., .. ­ ­ - L2 ­ // , 1992. . 30. 4. .435­454. 19. .., .., .. - L2 ­ // , 1987. . 25. 2. . 163­185. 20. Eismont N., Dunham D., Jen S.-C., Farquhar R. Lunar Swingby as a Tool for Halo-Orbit Optimization in Relict-2 Project // Proceeding of the ESA Symposium on Spacecraft Flight Dynamic, Germany, 30-4 October, 1991 (ESA SP-326, December 1991), pp.435-439. 21. .., .., .. L2 ­ ( "-2") // , 1993. . 31. 5. .3­20. 22. .. . . ­ .: , 1978. 23. . . . ­ : , 1982. 24. ., ., . . ­ .: , 1985. 25. GÑmez G., Jorba þ, Masdemont J.J., SimÑ C. Dynamics and Mission Design Near Libration Point Orbits. // Advanced Methods for Collinear Points. Volume 3. World Scientific, 2000.