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| Meirovitch L. — Methods of analytical dynamics |
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| Предметный указатель |
Frequencies, nonlinear system 299 300
Frequencies, nonlinear system, of combination tones 321
Frequencies, nonlinear system, of higher harmonics 321
Frequencies, nonlinear system, of subharmonic oscillation 320
Frequency, critical 393
Frequency, natural 19 298 302
Frequency, of symmetric gyroscope 384 388 392—393
from canonical systems 273—277
Function 497—501 505
Function, bounded 175 289
Function, class of 11 174
Function, continuous 497
Function, decrescent 290
Function, domain of 499
Function, homogeneous 232
Function, homogeneous, quadratic 74 137 232
Function, indefinite 232
Function, Lipschitz 174 289
Function, negative definite 232 289
Function, negative semidefinite 232 289
Function, positive definite 232 289
Function, positive semidefinite 232 289
Function, range of 499
Function, sign-constant or constant with respect to sign 232
Function, sign-variable or variable with respect to sign 232
Function, single-valued 499
Fundamental matrix 212 217 264 266
Fundamental set of solutions 212
Galilean reference frame See Reference system or frame
Galilean transformations 3—6
Galileo's law of inertia of 3 10
Galileo's principle of relativity 3
Gegenschein, as related to the three-body problem 424
Generalized coordinates 46—48 60 72 171
Generalized forces 61 75
Generalized impulse 80
Generalized momentum 80
Generalized momentum, conjugate 82
Generalized momentum, conservation of 82
Generating function 342 356 373
Generating solution 295
Geometry 1
Geometry of Euclid 1
Geometry of Riemann 2
Gimbal of gyroscope 382
Gimbal of gyroscope, inertia effect 386—389
Gimbal of gyroscope, walk 386
Gravitation, law of 11. See also Inverse square law
Gravitational potential energy 32 416 430—438 460
Gravitational torques 430—438
Gravity-gradient stabilized satellites 467 470—475
Group property 339 343
Gyrocompass 393—398
Gyropendulum 398—403
Gyroscope 381—406
Gyroscope, integrating 403—406
Gyroscope, oscillation of 382—386
Gyroscope, oscillation of, effect of gimbal inertia on 386—389
Gyroscope, oscillation of, effect of rotor shaft flexibility on 389—393
Gyroscope, rate 403—406
Gyroscopic forces 77
Gyroscopic forces, stability in the presence of 252—287
Gyroscopic motion 149 381—406
Gyroscopic systems 87 149
Gyroscopic terms 77 87
Half-trajectory, negative 174 199
Half-trajectory, positive 174 199
Hamilton — Jacobi equation 355—361
Hamilton — Jacobi equation, modified 357
Hamilton's canonical equations 91—97
Hamilton's canonical equations, for holonomic systems 94 172 243 273
Hamilton's canonical equations, for systems with nonconservative forces 95
Hamilton's canonical equations, for systems with nonholonomic constraints 95
Hamilton's canonical equations, for systems with nonpotential forces 95
Hamilton's canonical equations, stability of 243—252
Hamilton's characteristic function 360
Hamilton's principal function 334 356
Hamilton's principle 66—72
Hamilton's principle, application to continuous systems 70—72
Hamilton's principle, extended 68
Hamiltonian 94
Heliocentric reference frame 412
Herpolhode 149
Hessian matrix 93 230 274
Hill's equation 278—282
Hill's infinite determinant 280—282 285—286
Hill's infinite determinant, perturbation technique based on 309—313
Hohmann orbit 491
Holonomic constraint 51 55 61
Holonomic system 51
Homeomorphism 497 505
Identity transformation 343
Ignorable coordinate 34 82 85—88 249.
Impact parameter 38
Impulse, angular 13
Impulse, generalized 80
Impulse, linear 12 80
Impulsive forces 79—81
Impulsive moments 81
Inclination of orbit 412
Index of Poincare 195—197
Inertia 3 8
Inertia for rigid body, dyadic 130
Inertia for rigid body, ellipsoid 136
Inertia for rigid body, matrix 129
Inertia for rigid body, moments of 128
Inertia for rigid body, principal 136
Inertia for rigid body, products of 129
Inertia for rigid body, tensor 129 135
Inertial integrals 434
Inertial space or system 3 9 101
Infimum 177 234 243 501 502 504
Infinitesimal contact transformation 352—354
Infinitesimal stability 178 226 227
Infinitesimal upper bound 289
Instability 176
Instability of linear autonomous systems 222
Integral curve 174
Integral curve, bounded 175
Integral invariants 346—349
Integral invariants, absolute 347
Integral invariants, relative 347
Integrals of area 415
Integrals of motion 86. See also First integrals of motion
Integrating operator in method of averaging 323
Interval, closed 502 505
Interval, closed-open 502
Interval, open 502 505
Invariable plane of Laplace 415
Invariable plane of Poinsot 148
Inverse square law, gravitational 11 30—37
Inverse square law, of Coulomb 37—40
Isolated singular point 175
Jacobi integral 83 96 244 418
Jacobi — Liouville formula 214
Jacobian 180 336 348
Jordan canonical form 181 219 266
Jordan curve 195 498
Jordan curve theorem 195 506
Jump phenomenon 317—318
Kepler's equation 409—413
Kepler's planetary laws 4 11
Kepler's planetary laws, second law 28
Kepler's planetary laws, third law 36
Keplerian orbit 409 442 453 457
Kinematics 1
Kinematics of rigid body 123—126
Kinematics, Einsteinian 7
Kinematics, Lorentzian 6
kinetic energy 14
| Kinetic energy of rigid body 132—134 137
Kinetic energy of single particle 14
Kinetic energy of system of particles 24
Kinetic energy, rotational 133 137
Kinetic energy, translational 133
Krasovskii's theorem on asymptotic stability 237 241.
Krasovskii's theorem on instability 237 241
Kronecker delta, complementary 22 414
Kronecker delta, ordinary 22 103 414
Lagrange brackets 349—352
Lagrange multipliers 54 61 76 79
Lagrange's equations 72—81
Lagrange's equations for holonomic systems 74 77 171
Lagrange's equations for impulsive forces 79—81
Lagrange's equations for quasi-coordinates 157—160 400 467
Lagrange's equations for systems with nonconservative forces 76 88—91
Lagrange's equations for systems with nonholonomic constraints 77
Lagrange's equations for systems with nonpotential forces 76
Lagrange's libration points See Libration points of Lagrange
Lagrange's planetary equations 446
Lagrange's theorem 193 243—244
Lagrangian 68
Lagrangian configuration space 172
Lamellar force field 17
Least action, principle of 69 330—334
Legendre transformation 93 342
Level curves 190
Liapunov function 210 231
Liapunov function for linear autonomous systems 258—259
Liapunov's direct or second method 209 226
Liapunov's direct or second method, for autonomous systems 231—243 258—259 471—474 477—482
Liapunov's direct or second method, for nonautonomous systems 288—292
Liapunov's direct or second method, geometric interpretation of 239—243
Liapunov's theorem, first instability theorem 236 239—241 290
Liapunov's theorem, first stability theorem 234 239—240 290
Liapunov's theorem, on instability of conservative systems 193 245—246
Liapunov's theorem, on reducible systems 270
Liapunov's theorem, on stability of first-approximation equations 226—229
Liapunov's theorem, second instability theorem 236
Liapunov's theorem, second stability theorem 235 239—240 290
Libration 365
Libration points of Lagrange 424
Libration points of Lagrange, stability of 425—428
Libration, bounds of 481
Limit cycle 198—206
Limit cycle, semistable 199
Limit cycle, stable 198 199
Limit cycle, unstable 198 199
Limit point 200 503 504
Limiting set 200
Lindstedt's method 299—302
Linear basis 212
Linear manifold 211
Linear momentum 9 10 12
Linear momentum of rigid body 126—130
Linear momentum of system of particles 22
Linear momentum, conservation of 12 23
Linear systems 210—214
Linear systems, autonomous 217—224
Linear systems, fundamental matrix for 212
Linear systems, fundamental set for 212
Linear systems, general 210—217
Linear systems, homogeneous 210
Linear systems, linear basis for 212
Linear systems, nonhomogeneous 216 221
Linear systems, stability of 222—224 258—259
Linear systems, with periodic coefficients 264—270
Linear systems, with periodic coefficients, reducible 270
Linear systems, with periodic coefficients, stability of 268—269
Linear transformation of coordinates 102—104
Linearized equations 180
Liouville's theorem 338 349
Liouville's theorem, extended 343
Lipschitz condition 174 178
Lipschitz constant 174
Lipschitz function 174
Long-period perturbation of satellite orbit 461 462
Lorentz transformation 5—6 8
Lunisolar precession see Precession of the equinoxes
Many-body problem 413—416
Mappings 497 500
Mass 1—3 10
Mass, relativistic 8
Mathieu's equation 278 282—288 309—313
Mathieu's equation, principal instability region 313
Matrix, block diagonal 219
Matrix, companion 219
Matrix, determinant of 104 185 219
Matrix, diagonal 135 219
Matrix, exponential of 216
Matrix, fundamental 212 264
Matrix, Hessian 230
Matrix, identity, or unit 103
Matrix, inertia 129
Matrix, inverse or reciprocal of 103
Matrix, monodromy 265 274
Matrix, nonsingular 180 213 265
Matrix, of direction cosines 103
Matrix, periodic 264 270
Matrix, positive definite 233
Matrix, principal 213
Matrix, rotation 105 141
Matrix, similar 218
Matrix, skew-symmetric or antisymmetric 108
Matrix, stability 259
Matrix, symmetric 129
Matrix, symplectic 275
Matrix, trace of 185 219
Matrix, transpose of 103
Matrix, triangular 220
Mean anomaly 43 409
Mean motion 43 409
Mechanics, analytical 45
Mechanics, celestial 11 408
Mechanics, classical 1 9
Mechanics, Hamiltonian 329 339
Mechanics, Lagrangian 46 329 339
Mechanics, Newtonian 1—2 9
Mechanics, quantum 9
Mechanics, relativistic, or Einsteinian 7
Mechanics, variational approach to 46
Mechanics, vectorial 45
Member of a set 498. See also Element of a set
Mercury, motion of the perihelion 8 11—12
Metric spaces 501—503
Metrical properties 172
Michelson — Morley experiment 5
Minkowski space 7 8
Modified potential energy 32 88 247 418 422
Moment of a force See Torque
Moment of inertia 128
Moment of inertia, principal 136
Moment of momentum See Angular momentum
Moment-free rigid body, general case 147—149
Moment-free rigid body, inertially symmetric 143—147
Moment-free rigid body, stability of 228—229 238—239
Momentum, angular, or moment of 12 22.
Momentum, generalized 80
Momentum, integral 82 85—87 151
Momentum, linear 9 10 12 22.
Monodromy matrix 265 274
Motion space 173
Multipliers of Lagrange See Lagrange multipliers
Multiply periodic motion 369 373
Natural frequency 19 298 302
Natural system 77
Negative definite function 232 289
Negative semidefinite function 232 289
Neighborhood of a point 503 504
Neighborhood of a point, spherical 503
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