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| Goldstein H., Poole C., Safko J. — Classical mechanics |
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| Предметный указатель |
Generating function, infinitesimal rotation 404
Generating function, Poisson bracket 404 406
Generating function, symplectic 394
Generating function, table 373
Geodesic 40 324—326 362
Geodesic deviation 325
geoid 176
Geostrophic wind 178
Gibbs free energy 337
Glory scattering 114
Goldschmidt solution 64 65
Gradient 295
Gram — Schmidt method 249
Gravitational charge 226
Gravitational field 176 185 210 275
Gravitational quadrupole moment 226
Greek subscript convention 286
Group, abelian 606
Group, canonical transformation 387
Group, class 607
Group, conjugation 606
Group, cyclic 606
Group, definition 605
Group, dihedral 606 607
Group, generator 606
Group, Lorentz 282 610
Group, multiplication table 606
Group, properties 387 605—611
Group, quaternion 610
Group, representation 608
Group, rotation 171
Group, symmetry 412
Group, symmetry, for system 413
Group, symplectic 387 612
Group, theory 605
Gyration, radius of 198
Gyrocompass 223
gyromagnetic ratio 230
Gyroscope inertia 222
Gyroscope, torque free mounting 213
Hamilton — Jacobi theory and equation 334 430—451 488 528 549 619
Hamilton — Jacobi theory and equation, central force 448
Hamilton — Jacobi theory and equation, chaos 485
Hamilton — Jacobi theory and equation, completely separable 444
Hamilton — Jacobi theory and equation, cyclic coordinates 445—41
Hamilton — Jacobi theory and equation, ellipsoidal coordinates 479
Hamilton — Jacobi theory and equation, harmonic oscillator 434—439
Hamilton — Jacobi theory and equation, Kepler problem 445—451
Hamilton — Jacobi theory and equation, Kepler problem, spherical coordinates 451
Hamilton — Jacobi theory and equation, method 434—439
Hamilton — Jacobi theory and equation, new constant coordinates 432
Hamilton — Jacobi theory and equation, separation of variables 444—445
Hamilton — Jacobi theory and equation, two methods of solution 442
Hamilton's principle 34—36 44—50 313 324 355 562 564
Hamilton's principle, Lagrange's equations derivation 44 45
Hamilton's principle, Lagrange's equations derivation, modified 354 355 599
Hamilton's principle, nonholonomic systems 45—50
Hamiltonian 334—353
Hamiltonian as total energy 339
Hamiltonian covariant 349 352
Hamiltonian degrees of freedom 342
Hamiltonian density 573 586
Hamiltonian formulation 334—363
Hamiltonian formulation, advantages 51—54
Hamiltonian formulation, characteristic function 434 440—444
Hamiltonian formulation, comparison of characteristic and principal functions 442—443
Hamiltonian formulation, conservation theorems 347—349
Hamiltonian formulation, continuous systems 572
Hamiltonian formulation, cyclic coordinates 343—349
Hamiltonian formulation, generates canonical transformation 420
Hamiltonian formulation, Hamilton equations of motion 334—363 368 397 402
Hamiltonian formulation, Hamilton equations of motion, derived from variational principle 353
Hamiltonian formulation, Hamilton equations of motion, least action principle 356—363
Hamiltonian formulation, Legendre transformation derivation 334—342
Hamiltonian formulation, principal function 430—434 433 528
Hamiltonian formulation, principal function, compared with characteristic function 442
Hamiltonian formulation, relativistic formulation 349—353
Hamiltonian formulation, relativistic mechanics 349
Hamiltonian formulation, Routh procedure 347—349
Hamiltonian formulation, symplectic approach 339—343
Hamiltonian formulation, variational principle derivation 353—356
Hamiltonian generator of system motion 399
Hamiltonian perturbation 526
Hamiltonian quantum mechanics 613
Hamiltonian, Henon — Heiles 492 497 522
Hamiltonian, symplectic 576
Handedness convention 169
Hanon — Heiles chaos 484
Hanon — Heiles equipotentials 498
Hanon — Heiles galaxy model 516
Hanon — Heiles Hamiltonian 492 496 497 522
Hanon — Heiles islands in chaos 502
Hanon — Heiles potential 497
Hanon — Heiles, Hamilton equations 497
Hanon — Heiles, Poincare map 499—501
harmonic oscillator 434—440 485
Harmonic oscillator, action-angle variables 455 456 485
Harmonic oscillator, adiabatic invariant 550
Harmonic oscillator, canonical transformation 377
Harmonic oscillator, constants of motion 417
Harmonic oscillator, coordinate space plot 440
Harmonic oscillator, damped 269
Harmonic oscillator, damped, driven 505 507
Harmonic oscillator, ellipse 377
Harmonic oscillator, Feigenbaum plot 508
Harmonic oscillator, Hamilton — Jacobi 434—40
Harmonic oscillator, isotropic 82
Harmonic oscillator, isotropic, three dimensional 275
Harmonic oscillator, perturbation 529 542
Harmonic oscillator, phase diagram 380
Harmonic oscillator, Poisson brackets 417
Harmonic oscillator, relativistic 316
Harmonic oscillator, two dimensional 415 416
Harmonic oscillator, two dimensional, anisotropic 437
Heading angle 154
Heisenberg algebra 613
Heisenberg picture 408
Helmholtz free energy 337
Hermitean matrix 412
Herpolhode 202 203
Hertz principle of least curvature 361
Hierarchy of islands 504 505
High energy physics 300
Hodograph 131
Holonomic 12
Holonomic constraint 12
Holonomic system 199
Homogeneous function 320
Homogeneous problem 320 359
Homomorphism 418 609
Hooke's law 52 92 317 559
Hoop, rolling 50
Hoop, vertical 66
Huygens' waves 132
Hydrodynamic derivative 419
Hyperbola 81 316
Hyperbolic motion 315
Hyperbolic point 504
Hyperbolic region 504
Hypersurface 580
Hypersurface energy 494
Hypersurface, spacelike 580
Hypocycloid 64
Hysteresis 270 271 523
I.C.T. (infinitesimal canonical transformation) 385 386 402 403 408 410 413
Identity transformation 146 156
Ignorable see cyclic
Imbedding in chaos 514—516
Impact parameter 107
Inclination 532
| Incommensurate 548
Incommensurate, frequency, period 462 489 548
Incommensurate, oscillator 521
Inelastic collision 118
Inertia, ellipsoid 197 201
Inertia, tensor 191
Inertia, tensor, components 195
Inertia, tensor, diagonal 196
Inertia, tensor, eigenvalue 195 196
Inertia, tensor, eigenvector 196
Inertia, tensor, integral 194
Inertia, tensor, principal axes 196
Inertia, tensor, principal moments 197
Inertia, tensor, properties 195
Inertia, tensor, similarity transformation 196
Inertial force 5
Inertial system, definition 2
Infinitesimal canonical transformation 385 386 396 398 399 401
Infinitesimal rotation 163 166
Infrared spectroscopy 258
Instability 205
Integrability breakdown 502
Integral invariants of Poincare 394
Integral line 35
Integral variation 44
Integral, Jacobi 61
Integrating factor 15
Invariable plane 202
Invariance, adiabatic 549
Invariance, condition 594
Invariance, group 613
Invariance, logistic equation 484
Invariance, Lorentz 302
Invariance, Poisson bracket 388
Invariance, rotation 60
Invariance, scale 591
Invariance, translation 60
inversion 150 181
Islands in chaos 502 503
Islands, hierarchy 504 505
Islands, various orders 504
Isomorphism 609
J-matrix 342 382—389 393
J-matrix, Poisson bracket 388
Jabberwocky 202
Jacobi determinant 394
Jacobi form of least action pnnciple 361
Jacobi identity 393 398 424 428
Jacobi identity, integral 61 566 597
Jacobi identity, Lagrange brackets 424
Jacobi identity, Poisson bracket 390
Jacobi matrix of canonical transformation 426
Josephson junction 265 271 618
KAM (Kolmogorov — Arnold — Moser) theorem 484 487—492
Kamiltonian 370
Kepler equation 102 126 131
Kepler problem, action variables 471
Kepler problem, action-angle variables 466
Kepler problem, closed orbits, conditions 89—92
Kepler problem, cyclic coordinate 445
Kepler problem, equations of motion 72—76
Kepler problem, equivalent one body problem 70—71
Kepler problem, equivalent one dimensional problem 76—83
Kepler problem, inverse square law 92—96
Kepler problem, inverse square law potential 70—126 347 415
Kepler problem, Lie algebra 414
Kepler problem, motion in time 96
Kepler problem, orbit equation 86—89 96—103
Kepler problem, perturbation 536
Kepler problem, Poincare map 495 496
Kepler problem, scattering 106—121
Kepler problem, spherical polar coordinates 467
Kepler problem, symmetry group 414
Kepler problem, virial theorem 472
Kepler second law 73
Kepler third law 101 470
Kinematics, rigid body 134 184
Kinematics, tools 184
Kinetic energy, ellipsoid 203
Kinetic energy, rigid body 184
Kinetic energy, rotational 191
Kinetic energy, total 9
Kinetic theory 85 112
Kirchhoff junction conditions 66
Klein — Gordon equation 585
Klein — Gordon field 585
Klein — Gordon particle 596
Kolmogorov — Arnold — Moser (KAM) theorem 484 487—492
Korteweg-deVries equation 596 600
Kronecker delta ( ) 138 181 190
Laboratory frame 302
Laboratory system, transformation 306
Laboratory time 279
Lagrange bracket 392—394
Lagrange bracket, fundamental 393
Lagrange calculus of variations 36
Lagrange equations 16 21—23
Lagrange equations, derivation from Hamilton's principle 44 45
Lagrange equations, Euler equation derivation 200
Lagrange equations, Nielsen form 30
Lagrange equations, perturbation 533
Lagrange multipliers 16 67
Lagrange point 124
Lagrange solution of three body problem 123
Lagrange undetermined multiplier 198
Lagrangian, applications 24—29
Lagrangian, central force 71
Lagrangian, conserved quantities 566
Lagrangian, covariant 318 321 322 352
Lagrangian, definition 21
Lagrangian, density 564 567 583
Lagrangian, density, continuous system 561—566
Lagrangian, discrete system 558—560
Lagrangian, electromagnetic field 350
Lagrangian, formulation versus Newtonian 199
Lagrangian, from Hamilton's principle 44
Lagrangian, heavy symmetrical top 208
Lagrangian, precession of Earth 227
Lagrangian, relativistic 312
Lagrangian, rigid body 185 199
Lagrangian, separable 185
Laplace transform 264
Laplace — Runge — Lenz vector 102—106 131 429
Larmor frequency 231
Larmor precession 318
Larmor theorem 232
LC circuit 51
Least action principle 356 362
Least action principle,  -variation 359
Least action principle, Jacobi form 361
Least action principle, restrictions 358
Legendre polynomial 539
Legendre polynomial generating function 224
Legendre transformation 334 335 375 549
Levi-Civita density, ( ) 169 410
Liapunov exponent 491 519
Liapunov exponent, damped pendulum 519
Liapunov exponent, diagram 520
Liapunov exponent, dimension 521
Liapunov exponent, logistic equation 514 519
Liapunov exponent, negative 492
Liapunov exponent, Sierpinski carpet 519
Liapunov exponent, solar system 494
Libration 452 455 460
Lie algebra 171 412—415 611—613
Lie algebra, definition 412
Lie algebra, Kepler problem 414
Lie algebra, Poisson bracket 392
Lie algebra, structure constant 413 612
Lie bracket 171
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