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Goldstein H., Poole C., Safko J. — Classical mechanics |
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Предметный указатель |
-function 588
-variation 38
Kronecker delta 138 181 190
Levi-Civita density, permutation symbol 169 410
1-form 289
1-form, charge, current 295
1-form, covariant vector 290
1-form, definition 290
1-form, energy, momentum 295
1-form, figure 290
1-form, table 290
4-vector, energy, momentum 295 300 301
4-vector, photon momentum 304
4-vector, table 287
4-vector, velocity 286—288
4-velocity 286—288
Abbreviated action 354 434
Abelian group 606
Acceleration, centripetal 29 80
Acoustics 53 237 239
action 356
Action, abbreviated 359 434
Action, and reaction 7
Action, and reaction, strong law 7 10
Action, and reaction, weak law 5
Action, at a distance 323 583
Action, integral 359 596
Action, variable 452
Action, variable, integral over orbit 458
Action-angle variable 430 452—478 619
Action-angle variable, celestial mechanics 456
Action-angle variable, chaos 485
Action-angle variable, completely separable 457—466
Action-angle variable, degeneracy 73 464 468
Action-angle variable, harmonic oscillator 456
Action-angle variable, Kepler problem 466—478
Action-angle variable, one degree of freedom 452—457
Action-angle variable, periodic motion 452
Action-angle variable, perturbation 541
Action-angle variable, proper variables 481
Adiabatic invariance 549—555
Algebra 611
Algebra, Clifford 614 621
Algebra, geometric 617
Algebra, Heisenberg 613
Algebra, Lie 611 612.
Analogy, structural 54
Analytical mechanics 1
Angle variable 455
Angle variable, Fourier expansion 460
Angle variable, libration 460
Angle variable, quasi-periodic 461
Angle variable, rotation 461
Angle variable, time dependence 454 458 460
Angle variable, ultiply periodic 460
Angular momentum, areal velocity 73
Angular momentum, canonical 405
Angular momentum, central force problem 72
Angular momentum, conservation 3 72 73 571
Angular momentum, conservation, total 7
Angular momentum, delinition 2
Angular momentum, density, total 571
Angular momentum, eigenvalue 411
Angular momentum, electromagnetic 8
Angular momentum, ellipsoid 203
Angular momentum, mechanical 8 405
Angular momentum, Poisson bracket 408 411
Angular momentum, relativistic 309
Angular momentum, rigid body 188
Angular momentum, spherical symmetry 72
Angular momentum, spin 10
Angular momentum, total 8
Angular velocity in Euler angles 602 615
Anharmonic oscillator 545
Anomalistic year 131
Anomaly eccentric 100
Anomaly mean 102
Anomaly true 540
Antiproton 304
Antiquark 616
Aphelion 484
Approximation, semiclassical 115
Apsidal distance 78 95 96
Apsidal vector 86
Areal velocity 73
Ascending node 472
Astronomy, medieval 100
Attitude angle 154
Attractor 489 516 620
Attractor, regular 493
Attractor, strange 489 492 500
Attractor, strange, Henon — Heiles 500
Atwood's machine 27 28
Axis, rigid body 135
Axis, screw 161
Axis, semimajor 95 475
Axis, semiminor 101
Axis, symmetry 161
Azimuth 209
Backward glory 114
Bank angle 154 603
Barrier, centrifugal 112
Baryon 615 616
Basis vector 286
Bertrand's theorem 89 92
Bessel function 126
Biform 296
Bifurcation 454 484 505 513 514
Bifurcation diagram 506 508 513 515
Bilinear 219 388
Bilinear form 194
Binet ellipsoid 203 204
Biot — Savart law 7
Bivector 296
Black Box 121
Bohr quantum mechanics 466
Bohr theory 95
Boltzmann constant 185
Boltzmann factor 128
Boost 280. See also Lorentz transformation
Bounded motion 80 484
Boyle law 128
Boyle law and virial 84
Brachistochrone 42 63
C-O-M, center of momentum 301
Calculus of variations 36 43
Calculus, fundamental lemma 38
Calculus, operational 275
Canonical 338
Canonical equations of Hamiltonian 338
Canonical extended transformation 371
Canonical invariant 388
Canonical momentum 55 314
Canonical perturbation theory see Perturbation theory
Canonical relativistic 322 323
Canonical restricted transformation 371
Canonical transformation 348 368—121 619
Canonical transformation, active and passive 400 405
Canonical transformation, cyclic Hamiltonian 369 377 399 430 441
Canonical transformation, degeneracy 464 470
Canonical transformation, equations 368—375
Canonical transformation, examples 375—377
Canonical transformation, explicit time dependence 385 397 402
Canonical transformation, generated by Hamiltonian 420
Canonical transformation, generating function 373
Canonical transformation, group 387
Canonical transformation, harmonic oscillator 377—381
Canonical transformation, infinitesimal 385 402
Canonical transformation, invariant, phase space volume 393 420
Canonical transformation, invariant, Poisson bracket 389
| Canonical transformation, Jacobi matrix 382 394
Canonical transformation, parametric 385 405 408
Canonical transformation, restricted 371 381 382 387
Canonical transformation, symplectic 381—388
Canonical transformation, table of 373
Canonical variables 335 377
Cantor set 516 519 522
Capacitance 271
Caratheodory theorem 394
Carousel 183
Cartesian coordinates 25 141
Catenary 41 42 64
Cayley — Klein parameters 154 182 601 602
Celestial mechanics 533
Center of energy 312
Center of force 106
Center of gravity 185
Center of mass 5 6 185 312
Center of momentum 301 312
Center of momentum, system 301
Central force problem 70—126. See also Kepler problem
Centrifugal barrier 112
Centrifugal effect 126
centripetal acceleration 29 175
Chain rule 18
Chandler wobble 208 228
Chaos 483 522 617 619
Chaos, attractor 489—491
Chaos, bifurcation 505—509
Chaos, damped harmonic oscillator 505—509
Chaos, dimensionality 616 522
Chaos, fractals 516—522
Chaos, Henon — Heiles 496—503 506
Chaos, Islands 503—505
Chaos, KAM theorem 487—189
Chaos, logistic equation 509—516
Chaos, motion 491
Chaos, onset 492 501 503
Chaos, parametric oscillator 508
Chaos, parametric resonance 509
Chaos, perturbation theory 487—489
Chaos, properties of 491
Chaos, trajectory 491 494 521 522
Character table 611
Characteristic equation 157
Characteristic value 156
Charge density 588
Charged particle in electromagnetic field 23 317 553
Charm 615 616
Chasles' theorem 161 184
Class of group 607
Classical mechanics 1—600
Clifford algebra 614 621
Closed orbit 89 452
Colliding beam 304
Collision, elastic 118 120 306
Collision, inelastic 118
Commensurability 463
Commensurability, condition 464
Commensurate 105 463
Commensurate, completely 464
Commensurate, condition 464
Commensurate, frequency 462
Commensurate, m-fold 464
Commutator 171 411
Commutator, quantum mechanics 392 398
Commutator, relations 170
Configuration space 34 357
Configuration space, point transformation 370
Configuration space, variation 36
Congruence transformation 245 246 252
Conic section 94 99
Conjugate momentum 55 335 351
Conservation differential theorem 594
Conservation energy function 62
Conservation momentum 403
Conservation theorems 7 55 72 343 597
Conservation theorems, angular momentum 3 344
Conservation theorems, canonical momentum 315 340
Conservation theorems, energy 4 11 345 450
Conservation theorems, linear momentum 2 6 344
Conservation theorems, Noether's theorem 589
Conservation theorems, Poisson bracket 396 402
Conservation theorems, relation to symmetry properties 54—59
Conservation theorems, system of particles 6
Conservation theorems, total 7
Conservative system 4
Conserved current 594 595
Constant of motion 105 397 402 403 415
Constant of motion, algebraic 418
Constant of motion, central force 105
Constant of motion, Jacobi identity 397 411
Constant of motion, Poisson bracket 398
Constraint 12—16 24
Constraint, differential 16
Constraint, equation 15
Constraint, holonomic 12
Constraint, nonholonomic 12
Constraint, nonintegral 16
Constraint, rheonomous 13
Constraint, rigid body 12
Constraint, rolling 182
Constraint, schleronomous 13 25
Constraint, semiholonomic 46 49
Constraint, virtual work 16 17 48
Constraint, weak 321
Continuity conditions 572
Continuity equation 595
Continuous system 265 558 568
Continuous system, Hamiltonian formulation 572—577
Continuous system, Lagrangian density 561—566
Continuous system, stress energy tensor 566—572
Continuous system, transition from discrete to continuous 558—561
Contour integration 469
Contraction 290 295
Contraction of tensor 191
Contravariant 289
Control parameter 503 506
Control parameter, logistic equation 510
Coordinate, basis 286
Coordinate, Cartesian 184
Coordinate, contraction 295
Coordinate, cyclic 55 343 369 445
Coordinate, generalized 13 19 239
Coordinate, internal 272
Coordinate, mass weighted 241 258
Coordinate, normal 251 257 259
Coordinate, polar 72
Coordinate, pseudo-Cartesian 294
Coordinate, rotating 175
Coriolis 174—179
Coriolis acceleration 176
Coriolis circulation of fluid dynamics 177
Coriolis deflection 176—178 182
Coriolis effect 126 174—179 326
Coriolis effect on meteorological phenomena 177
Coriolis force 175
Coriolis hemisphere 178
Coriolis pressure gradient 176
Coriolis, Foucault pendulum 179
Correspondence principle 325 390 392 398
Correspondence principle, Poisson bracket 388 391 392 398
Cosmological constant 328
Cosmology 617
Coulomb field 109 111
Coulomb law 274
Coulomb scattering 110
Coupled electrical circuits 53
Covariant definition 277
Covariant equation 297
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