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| Thomas T. Y. — The elementary theory of tensors with applications to geometry and mechanics. |
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| Предметный указатель |
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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