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| Авторизация |
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| Поиск по указателям |
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| Ardema M.D. — Analytical Dynamics: Theory and Applications |
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| Предметный указатель |
Acceleration of a point 4
Acceleration, possible 77
Accessibility of configuration, space 59
action 95
Actual motion 53
Angular acceleration 9
Angular velocity 9 18
Apoapsis 185
Assumptions, basic 1
Autonomous systems 47
Basic kinematic equation 10
Basic problems in kinetics 3
Bertrand’s theorem 235
Calculus of variations 90
Canonical equations 263
Carnot’s theorem 240
Center of mass 17
Central force motion 272
Central principle 86
Characteristic equation 212
Choice of coordinates 131
Classification of constraints 154
Classification of forces 80
Configuration space 49
Conic sections 183
Conservative force 14 78 113 119
Constrained particle 136
Constraint forces 66 68
Constraints, acatastatic 57
Constraints, catastastic 57
Constraints, configuration 56
Constraints, equality 56
Constraints, holonomic 51 57
Constraints, nonholonomic 51 56 137
Constraints, rheonomic 51
Constraints, scleronomic 51
Contact transformations 283
Continuous group of transformations 281
Continuous point transformations 287
coordinates 102
Coordinates, cylindrical 8 133
Coordinates, generalized 102
Coordinates, rectangular 132
Coordinates, spherical 8 135
Degrees of freedom 19 53
Descriptive function 120 264 301
Differential 76
Dirichlet’s stability theorem 221
Displacements, actual 66
Displacements, infinitesimal 54
Displacements, possible 66 104
Displacements, virtual 66 104
Disspative forces 156
distribution 225
DuBois - Reymond lemma 91
Dynamic coupling 122
Dynamics 3
Dynamics, problem of the first kind 3 48 65
Dynamics, problem of the second kind 3 48
d’Alembert’s principle 67
Eccentric annomaly 186
Eccentricity 183
Eigenvalues 212
Embedding constraints 124
Energy theorem 235
Euclidean space 1
Euler - Lagrange equation 90
Euler angles 191
Euler’s theorem 11
Event space 49
Extremal 90
Formulating problems 131
Functions, Liapunov 220
Functions, positive definite, definite, semi-definite, negative definite 219
Fundamental equation 67 78 112 228 232 249 262
Fundamental lemma 90
Gauss’s principle of least constraint 233
General potential functions 121
Generalized force 112
Generalized goordinates 102
Generalized momentum 158
Generating function 283
Gibbs — Appell equations 250
Gibbs’ function 249
Gibbs’ theorem 250
Given forces 66 78
Gradient 13
Gravitation 14
Gravitational constant 14
Gyrocompass 201
Gyroscope 199
Hamilton 307
Hamilton — Jacobi equation 304
Hamilton — Jacobi theorem 305
Hamiltonian function 262
Hamilton’s characteristic function 309
Hamilton’s equations 263
Hamilton’s principal function 298
Hamilton’s principle 87 117 122 297
Hamilton’s principle, first form 87
Hamilton’s principle, second form 87
Hamilton’s principle, third form 88
Heavy symmetrical top 192 315
Hill equations 217
Homogeneous contact transformations 286
Ignorable coordinates 158 282
| Impulsive constraints 228 229
Impulsive constraints, inert 232
Impulsive constraints, live 232
Impulsive force 225
Inertial reference frame 1
Infinitesmal contact transformations 330
Integrals of motion 150
Invariance of Lagrange’s equations 123
Inverse square forces 182
jacobi 308
Jacobi’s integral 153
Jacobi’s integral, explicit form 153
Jacobi’s theorem 291
Jacobi’s theorem of the last multiplier 277
Kelvin’s theorem 237
Kepler’s laws, first 183
Kepler’s laws, second 180
Kepler’s laws, third 184
Kinematics 3
kinetic energy 13 83 109
Kinetics 3
Koenig’s theorem 21
Koenig’s theorem, analogue of 253
Lagrange 118
Lagrange brackets 288
Lagrange multipliers 70
Lagrange’s equations 117
Last multiplier 276
Liapunov’s theorem 220 222
Liouville systems 162
Liouville’s theorem 288
Mean anomaly 186
Mechanical energy 16
Momentum integral 159
Multiplier rule 70 115 116
Natural systems 263
Newtonian problem 47 225
Newton’s laws of motion 1 2
Newton’s Second Law 47
Non-minimal coordinates 121
Nonconservative forces 78
Noncontemporaneous variations 95
Normal-tangential components 5
Nutation 192
One-to-one 103
Onto 103
Orbit equation 182
Orbits, hyperbolic, parabolic, elliptical, circular 183
Particle dynamics 4
Periapsis 185
Pfaffian form 57 68
Poisson brackets 271
Poisson’s theorem 272
Possible motion 53
potential energy 13 113
Potential energy function 78
Power 12
Precession 192
Precession of the equinoxes 199
Principle of least action 94
Principle of least action, Jacobi’s 96
Principle of least action, Lagrange’s 95
Qualitative integration 151
Quasi-coordinates 246
Radius of curvature 7
Rayleigh’s dissipation function 120
Rectangular components 4
Relative velocity 9
Relativity theory 28
Rigid body 18 53 67
Rigid body dynamics 17
Routh — Hurwitz criteria 212
Routhian function 159
Separability 314
Separation of variables 162
Solution of dynamical system 151
Solution, closed form 151
Solution, in quadratures 151
Speed 4
Spin 192
Stability 206
Stability, Hamiltonian systems 268
Stability, Liapunov 208
Stability, orbital 210
Stability, Poincare 209
State space 50
State variable form 206
State vector 206
State-time space 50
Statics 3
Strictly Newtonian problem 47
Superposition theorem 234
Taylor’s Theorem 238
Time equation 186
Transformation of coordinates 102
True anomaly 185
Unconstrained particle 132
Uncoupled systems 162
Variation of a function 76
Variation of constants 319
Variation of the elements 325
Velocities, possible 77
Velocity of a point 4
Virtual change of state 74
Virtual velocity 74
Virtual work 66 76
Work 12
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