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Thomas T. Y. - The elementary theory of tensors with applications to geometry and mechanics.
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Название: The elementary theory of tensors with applications to geometry and mechanics.Автор: Thomas T. Y. Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: 1stГод издания: 1931Количество страниц: 130Добавлена в каталог: 20.11.2012Операции: Положить на полку |
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Accelerations 58 83 Accelerations, center of 85 Accelerations, centripetal 84 Accelerations, composition of 58 Accelerations, tangential 85 Accelerations, transformation of 58 Action and Reaction, Principle of 95 Amplitude 105 Angle of rotation 64 Angle, definition 38 Angular velocity 77 Area of parallelogram 43 Axes, central 71 Axes, coordinate 28 Axes, instantaneous, central 74 80 Axes, right-handed and left-handed 39 Axis of rotation, definition 64 Axis of rotation, instantaneous 74 76 Base point, definition 69 Bocher 1 Center of acceleration 85 Center of gravity 107 Center of oscillation 107 Center of rotation 68 81 Center of suspension 107 Central Axis 71 Central axis, instantaneous 74 80 Central axis, surfaces generated by 81 Central motion 60 113 centripetal acceleration 84 Compound pendulum 107 Configurations, congruence of 26 Conical pendulum 112 Constraints 100 coordinates 14 15 Coordinates, allowable system of 89 Coordinates, Cartesian 27 Coordinates, generalized 100 Coordinates, origin of 29 Coordinates, orthogonal transformation of 40 Coordinates, rectangular Cartesian 27 38 Coordinates, transformation of 15 39 Coriolis, acceleration of 86 Coriolis, theorem of 85 Critical velocity 115 Curl of a vector 51 Derivatives, definition 3 Determinants, definition 8 Determinants, functional or Jacobian 16 Determinants, minors and cofactors of 10 Determinants, multiplication of 11 Differentials 6 20 Dimensional formulae 97 Direction cosines 28 Direction numbers 28 Displacements of rigid bodies 29 31 63 66 68 70 Displacements, composition of 72 Displacements, instantaneous screw 74 80 Displacements, screw 70 Displacements, virtual 102 Distance, mean 115 Distance, measurement of 34 Divergence of a vector 47 Dynamical principle of relativity 89 Dynamical systems, definition 88 Dynamical systems, degree of freedom of 101 Dynamical systems, holonomic 101 Dynamical systems, non-holonomic 101 Dyne 92 Eddington, A.S. 90 Einstein, A. 43 53 90 Elliptic-harmonic motion 59 105 energy equation 116 Equations, Lagrange's 101 Equations, parametric 27 Equations, solution of linear 11 Euclidean principle of relativity 42 Fine 1 Force, definition 92 Force, generalized 102 Force, mutual independence of 94 Force, unit of 92 Functions 2 Functions, Euler's theorem on homogeneous 6 Functions, point 19 Functions, rational 30 Generalized coordinates 100 Generalized force 102 Geometry, Euclidean 25 47 Geometry, physical 25 Gram 92 Gravitational constant 96 Group of transformations, definition 42 Group of transformations, kinematical 55 Group of transformations, orthogonal 39 Holonomic dynamical systems 101 Infinitesimals, definition 2 Integrals, definition of indefinite and definite 7 Integrals, double and triple 8 Integrand, definition 7 Invariant theoretic viewpoint 45 Invariants, scalar 46 Invariants, vector 49 Kepler's laws of planetary motion 115 Kinematical group of transformations 55 Kinematical principle of relativity 54 Kinetic energy, definition 103 Kinetic potential, definition 103 Kronecker's delta 17 Lagrange's equations 101 Lagrange's equations, transformation theory of 117 Lagrangian function, definition 104 Lamb 115 Length, unit of 37 Lines, direction of 28 Lines, equations of 27 Lines, world 56 Lorentz transformation 90 Mass, Mach's definition of 91 Mass, unit of 92 Matrix, augmented 12 Matrix, definition 9 Matrix, determinants of 10 Mean Solar Day 54 Meter, International 37 Moment of inertia 107 Motion, central 60 113 Motion, curvilinear 55 59 Motion, elliptic-harmonic 59 105 Motion, plane 66 81 Motion, rectilinear 59 Motion, simple-harmonic 59 61 105 Newtonian dynamics 88 Newtonian law of gravitation 96 Non-holonomic dynamical systems 101 Orthogonal transformations of coordinates 39 40 Pendulum, compound 107 Pendulum, conical 112 Pendulum, double 106 Pendulum, simple 99 104 Phase 105 Pitch of screw displacement 17 81 Plane motion 66 81 Plane, coordinate 28 Plane, equation of 28 POINTS 1 14 Points, base 69 Points, motion of 55 Points, transformation of 39 Potential energy, definition 103 Principle of action and reaction 95 Principle of relativity, dynamical 89 Principle of relativity, Euclidean 42 Principle of relativity, kinematical 54 Rigid body, accelerations in 83 Rigid body, continuous motion of 73 Rigid body, definition 26 Rigid body, degree of freedom of 61 Rigid body, displacements of 29 31 63 66 68 70 Rigid body, general motion of 79 Rigid body, velocities in 73 Rotations about a fixed point 63 74 Rotations about an axis 64 74 76 Scalar invariant, definition 46 Scalars, definition 19 Screw displacement 70 Screw displacement, instantaneous 74 80 simple pendulum 99 104 Space 14 Space, dimensionality of 14 26 Space, Euclidean 25 Space-time representation 56 Special theory of relativity 54 90 Summation convention 16 Tangential acceleration 85 Tensors, addition of 23 Tensors, contraction of 24 Tensors, definition 22 Tensors, differentiation of 48 Tensors, multiplication of 23 Tensors, special 48 Tensors, symmetric and skew-symmetric 24 Time 52 Time, origin of 53 Time, unit of 53 54 Trajectory of moving point 55 Transformations, coordinate 15 39 Transformations, group of 42 Transformations, point 39 Translation 68 Translation, velocity of 79 Variables 1 Vector invariant, definition 49 Vector product 49 Vectors, addition of 21 Vectors, curl of 51 Vectors, definition 20 Vectors, divergence of 47 Vectors, equality of two 21 Vectors, length of 47 Vectors, scalar product of two 22 Vectors, vector product of two 48 Velocities 57 73 Velocities, angular 77 Velocities, composition of 58 Velocities, critical 115 Velocities, moment of 111 Velocities, parallelogram law of addition of 59 Velocities, transformation of 58 Virtual displacements 102 Volume of tetrahedron 44 Weight, definition 94 Weyl, H. 90 Whittaker 70 Work 102 World line 56
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