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Hand L.N., Finch J.D. — Analytical Mechanics
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Íàçâàíèå: Analytical MechanicsÀâòîðû: Hand L.N., Finch J.D. Àííîòàöèÿ: This introductory undergraduate text provides a detailed introduction to the key analytical techniques of classical mechanics, one of the cornerstones of physics. It deals with all the important subjects encountered in an undergraduate course and thoroughly prepares the reader for further study at graduate level. The authors set out the fundamentals of Lagrangian and Hamiltonian mechanics early in the book and go on to cover such topics as linear oscillators, planetary orbits, rigid-body motion, small vibrations, nonlinear dynamics, chaos, and special relativity. A special feature is the inclusion of many "e-mail questions," which are intended to facilitate dialogue between the student and instructor. It includes many worked examples, and there are 250 homework exercises to help students gain confidence and proficiency in problem-solving. It is an ideal textbook for undergraduate courses in classical mechanics, and provides a sound foundation for graduate study.
ßçûê: Ðóáðèêà: Ôèçèêà /Êëàññè÷åñêàÿ ôèçèêà /Òåîðåòè÷åñêàÿ ìåõàíèêà /Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö ed2k: ed2k stats Ãîä èçäàíèÿ: 1998Êîëè÷åñòâî ñòðàíèö: 574Äîáàâëåíà â êàòàëîã: 19.06.2005Îïåðàöèè: Ïîëîæèòü íà ïîëêó |
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Ïðåäìåòíûé óêàçàòåëü
Local chaos 442 451 Locomotive (prob) 267 Logistic map 425 481—492 474 Lorentz 494 Lorentz contraction 500 Lorentz force 199 508 537—539 Lorentz invariant 521—526 538 Lorentz invariant, action 530—532 Lorentz invariant, charge 508 534 Lorentz invariant, invariance theorems 524 Lorentz invariant, mass 519 527 Lorentz invariant, Planck's constant 512 Lorentz invariant, proper time 527 Lorentz transformation 498—501 503—504 555—556 544 Lorentzian line shape 109 Lorenz equations (prob) 477 Lyapuinov conservative systems 449—450 Lyapuinov dimension See dimension Lyapunov Lyapuinov dissipative systems 458—459 467 471—472 Lyapuinov logistic map 483 485—486 Lyapunov time 471 m-cycle, logistic map 481 Mach's principle 323—325 Mach, E. 324 513 528 MACHOS 155 Maclaurin 342 Magnetic field 493 509—510 522 (30 74 277 550—551) Magnetic field, charged panicle See particle in electric and magnetic fields Magnetic field, relativistic particle See particle in a magnetic field relativistic Magnetic force, transformation Law See transformation law electric Magnification See dimension magnification Manifold, stable 440 446 Manifold, unstable 440 446 Map, area-preserving 431—432 Map, logistic See logistic map Map, Poincare section 434 439—440 Map, standard (prob) See standard map (prob) Map, tangent See stability matrix Marginal stability See stability marginal MARS See solar system stability Mass, definition of 512—513 Mass, inertial 324 Mass, reduced 136—137 Mass, rest 513—517 Matching boundary conditions 96—98 Mathematical Principles of Natural Philosophy 133 Mathieu equation 383 395—398 Mathieu functions 397 Matrix, antisymmetric See antisymmetric matrix Matrix, hermitian See Hermitian matrix Matrix, identity See identity matrix Matrix, mondronomy See stability matrix Matrix, notation 262 Matrix, orthogonal 263 Matrix, stability See stability matrix Matrix, transformation 265 Matrix, unitary See unitary matrix Maupertuis 55 339 Maupertuis' Principle 75—80 (74 162) Maupertuis, cannonball trajectory 77 Maxwell, J. 493 Mayer 514 Mechanique Analitique 23 86 Mercury See solar system stability Mercury, precession of 154 Method of matching boundary conditions 96—98 Method of successive approximations See successive approximations method 356 Metric tensor 51 529 Michclson — Moriey experiment (prob) 551 Milankovitch, M. 323 Minimal action principle of Maupertuis See Maupertuis' Principle Minimal optical pain for light 55 Minkowski 495 501 Mixer 402 mks units See SI units MODE See normal mode Mode, amplitude ratio See mode displacement ratio Mode, displacement ratio 343 346 352 353—355 357 361 363—367 Mode, frequency 343 353 357 352—366 374 Mode, vector 352 355 362—367 Mode-tacking See phase locking Molecule, diatomic (prob) See diatomic molecule (prob) Molecule, diatomic linear See triatomic molecule linear Moment of inertia tensor See inertia tensor Momental ellipsoid See ellipsoid momental Moments, principal See principal moments Momentum conservation 519 Momentum conservation, space 189—190 201—202 Momentum conservation, space, Lagrangian 190 Momentum, canonically conjugate See canonically conjugate momentum Momentum, relativistic 517—519 547 Momentum, transverse, relativistic 517 532 548 Mondronomy matrix See stability matrix Moon See solar system stability Moser See KAM theorem Multiplicative ergodic theorem See Oseledic's multiplicative ergodic theorem Mylar, aluminized 517 n-torus See torus Neutral equilibrium See equilibrium neutral Neutral fixed point See fixed point neutral Neutrinos 155 528 Newton's second law 2 5 17 512—513 Newton's Third Law 3 Newton, Isaac 45 132—133 284 299 324 339—342 423 468 493 Newtonian mechanics, review with sliding block example 1—3 Noetber, Emmy 172 Noether's theorem 172—175 245 Nonconservative force 90 Nonconservative force, example of a rubber band 42—43 Nonconstraint force 5 Nondissipative chaos See chaos in Nonholonomic constraints See constraints nonholonomic Noninertial reference frames See reference frames noninertial Nonintegrable 36 63 207 237 305 425 442 447—448 451—452 Nonlinear oscillator See oscillator nonlinear Nonlinear pendulum See pendulum nonlinear Nonlinear resonance 425 Nonlinear resonance, double pendulum 440—442 Normal coordinates 343 359 Normal mode 343 352—355 Normal mode frequency See mode frequency Normalization 338 356—357 North pole 339—340 Nuclear magnetic resonance 277 Nutation 316 333 Oblate ellipsoid See ellipsoid oblate Obliquity 317 Obliquity, chaotic of Earth 474 ODE See differential equation ordinary One-dimensional systems 123—125 158 Orbital period 147 Orbits, of Kepler problem 143—151 Order of infinity See infinity orders Ordinary differential equation See differential equation ordinary Orthogonal matrix 263 277—278 Orthogonal modes 355—356 Orthogonal transformation 288 302 336 Oscillations, harmonic See harmonic oscillations Oscillations, small See small oscillations Oscillations, subharmonic See subharmonic oscillations Oscillator, anharmonic See anharmonic oscillator Oscillator, damped 81 Oscillator, damped simple harmonic 90—94 103 106—110 116—120 Oscillator, damped simple harmonic, complex driving force, steady state 108 Oscillator, damped simple harmonic, critically damped 92 Oscillator, damped simple harmonic, overdamped 92 Oscillator, damped simple harmonic, response to sinusoidal driving force, relative phase 110—113 Oscillator, damped simple harmonic, underdamped 91 Oscillator, driven 81 94—113 Oscillator, driven, damped simple harmonic (prob) 120—121 Oscillator, driven, simple harmonic (proh) 119 Oscillator, Duffing See Duffing oscillator Oscillator, linear See osclllaior simple Oscillator, nonlinear 125—127 121—122 Oscillator, simple harmonic 81 88—90 124 212—213 218 237—239 (115 202 240 246 551) Oscillator, simple harmonic response to sinusoidal driving force 106 Oscillator, simple harmonic, general solution with Green's function 99—102 105 Oscillator, simple harmonic, Hamiltonian See Hamiltonian oscillator simple Oscillator, simple harmonic, steady-state solution 95 97—98 107-J08 Oscillator, simple harmonic, step function drive force 96—99 Oscillator, simple harmonic, stored energy 94 109 Oscillator, simple harmonic, transient solution 95 97—98 107—108 Oseledic's multiplicative ergodic theorem 449 Overdamped See oscillator damped parabola 144 Parabolic orbits 145 164 Parallel axis theorem 289 parallel plate capacitor 508—510 Parametric amplification 384 Parametric amplifiers 390 Parametric resonance 334 388—398 414—419 Parametric resonance, unstable 397 Particle decay 528 546 Particle decay, in a gravitational Meld, Hamiltonian — Jacobi equation 220—222 224—228 Particle decay, in a magnetic field 30 74 Particle decay, in a magnetic field, relativistic 539—540 Particle decay, in electric and magnetic fields, Lagrangian and Hamiltonian 192 Particle decay, on a parabolic wire, Hamiltonian 182—183 Particular solution See oscillator steady-state Pendulum See also oscillator [33—34 116—117 373 415 419] Pendulum (prob), physical See physical pendulum (prob) Pendulum (prob), triple See triple pendulum (prob) Pendulum, action-angle variables 231—232 Pendulum, damped driven See damped driven pendulum Pendulum, double See double pendulum Pendulum, equilibrium 82—83 Pendulum, linear 58—59 Pendulum, nonlinear 125—130 Pendulum, nonlinear, libration 126 Pendulum, nonlinear, period 128—130 Pendulum, nonlinear, phase portrait 127—128 Pendulum, nonlinear, rotation 126 Pendulum, spherical See spherical pendulum Pendulum, spring See spring pendulum Pendulum, two coupled 344—348 376—377 Pendulum, upside-down See upside-down pendulum Pendulum, with driven support 388—398 414 Penny example 62—64 73 Perihelion, ellipse See ellipse perihelion Period doubling 456—458 483—485 Period doubling, cascade 457 Period of elliptical motion See elliptical motion period Period, anharmonic oscillator See anharmonic oscillator period Period, Duffing oscillator See Duffing oscillator period Period, nonlinear pendulum See pendulum nonlinear Period, orbital See orbital period Perpetual motion machine 514 Perturbation 383 384—388 433 439 442 Perturbation theory 398 404—408 Perturbation theory, Lindstedt — Poincare See Lindstedt — Poincare perturbation theory Phase advance 390 393 Phase portrait (prob) 156—158 Phase portrait, pendulum See pendulum nonlinear phase Phase space 127 203—204 248 Phase space, density 186—189 Phase trajectories 127- 128 424 Phase trajectories of damped drive pendulum 454—457 461—462 phase velocity 526 Phase-locking 425 461 Phenomenological 453 Photon disintegration (prob) 546 Physical pendulum (prob) 32 34 157 332 Pitchfork bifurcation See bifurcation pitchfork Planck energy frequency relation 512 Planet, perturbed by Jupiter (prob) See asteroid perturbed Planetary orbits (prob) 162—164 Pluto See solar system stability Poincare 423—424 426 428 433 439 447—448 468 494 Poincare recurrence theorem 204—206 Poincare section 393 428—436 442—443 445 451 459 Poincare section, damped driven pendulum 454—457 462—463 Poincare section, double pendulum 430—433 435 441 451 Poincare section, section map See map Poincare Poincare — Birkhoff theorem 439—442 Poincare — Hopf theorem 235 Poinsot construction 283 307—312 Poinsot, L. 306 Point mass sliding on a bowling ball 38—39 Point masses, N connected by a string 367—371 379 Point masses, transformation 208 216 Poisson brackets 207 217—218 236—237 251 243—245 Polaris 317 Polhode 308 311—312 Positive definite 288 337 351 Positronium acceleration (prob) 550 Postulates, of special relativity See special relativity two potential energy 18—19 42 85—86 (See Potential energy for the earth in a gravitational field 318 Potential energy matrix, Taylor series near equilibrium 350 Potential, effective See effective potential Poynting vector 507 517 Precession 273 295—298 315—316 321 Precession of equinoxes See equinoxes precession Precession of Foucault pendulum See Foucault pendulum Precession of Kepler ellipses (prob) See Kepler ellipses precession Precession of Mercury 154 Precession of symmetric heavy top 313—316 Precession of torque free top See symmetric top torque asymmetric torque Precession, retrograde 317 Pressure, radiation See radiation pressure Primed frame 260 Principal axis 283 292 306 339 Principal axis, transformation 288 Principal moments 288 Principia 133 340 474 Principle of least action See Hamilton's Principle of Relativity 493^494 Processing orbits 154 Prolate ellipsoid See ellipsoid prolate Proper time 527 331 Proper time for a particle in a constant force 536—537 Proton-proton annihilation 517—518 Pseudovector 257 277 Ptolemy 130 317 Pumping a swing (prob) 416 Pythagorean Theorem 50 q See quality factor Quadratic form 22 351 29 Quadrature 22 125 Quality factor 90 93—94 453 quantum mechanics 44 229—230 67 Quasiperiodec 238 Quasiperiodec, route to chaos 428 Radiation pressure 517 Radiation reaction force 533 Radiofrcquency resonant cavity 185 Rank, of tensor 333 Rapidity (prob) 544 Rational winding number See winding number rational Reduced echelon form 337 Reduced mass 137 Reference frames 495 Reference frames, body 260 (see also body coordinate system) Reference frames, inertial See inertial reference frames Reference frames, linearly accelerated 193—195 Reference frames, noninertial 20 Reference frames, noninertial (prob) 200 Reference frames, rotated See rotated reference frames Reference frames, rotating See rotating reference frames Reference frames, space 260 See Reflection 257 (see also transformations discrete)
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