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Hand L.N., Finch J.D. — Analytical Mechanics
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Название: Analytical MechanicsАвторы: Hand L.N., Finch J.D. Аннотация: 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.
Язык: Рубрика: Физика /Классическая физика /Теоретическая механика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1998Количество страниц: 574Добавлена в каталог: 19.06.2005Операции: Положить на полку |
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Предметный указатель
Reflection, hyperbolic fixed point 446 Refractive index (prob) 69 Regular motion 425 447 451 Relative phase 110—113 Relativistic action 530—532 Relativistic action, circular motion 539—540 Relativistic action, energy See energy relativistic Relativistic action, Hamiltonian 533 Relativistic action, Lagrangian 550—551 (prob) Relativistic action, Lagrangian mechanics 530—540 Relativistic action, Lagrangian, electromagnetic field 534—536 Relativistic action, Lagrangian, free particle 532 Relativistic action, mechanics 494 (see also special relativity) Relativistic action, momentum See momentum relativistic Relativistic action, velocity See velocity transformation rules relativistic Relativity, general See general relativity Relativity, of simultaneity See simultaneity Relativity, special See special relativity Renormalization 486—490 Repulsive force, hyperbolic orbits See hyperbolic orbits repulsive Resonance 105—110 Resonance, nonlinear See nonlinear resonance Resonance, parametric See parametric resonance Resonant cavity, radiofrequency See radiofrequency resonant cavity Resonant frequency, See frequency resonant Resonant terms 400 (see also secular terms) Rest frame, instantaneous See instantaneous rest frame Rest mass 513—517 Restricted three-body problem (prob) See three-body problem restricted Retrograde precession See precession retrograde Rheonomic constraint See constraints rheonomic Rigid body 254—255 Rigid body, as collection of mass points 11 Rigid body, kinetic energy 284—286 Rigid body, motion 283—325 Rigid body, torque free motion See Euler's equations Rotated reference frames 259—263 Rotating reference Frames 190—192 263—264 266 Rotating turntable (prob) 243 Rotation matrix 259—263 255 257—259 Rotation matrix of hurricanes See hurricanes Rotation matrix of pendulum See pendulum nonlinear Rotation matrix, infinitesimal 171 254—259 Rotation matrix, number See winding number Rotational angular momentum, See angular momentum rotational Rotational invariance See invariance rotational Rotational kinetic energy See kinetic energy rotational Rotations 261—263 302 Rotations, simultaneous See simultaneous rotations Rotations, three-dimensional 239 261 Rotator 289 Routhian 23 [35 197 331 377] Row elimination 347 355 380 Row elimination, reduction See Gauss — Jordan elimination Rubber band 42—43 Rutherford 151 Rutherford, scattering 151—152 165—167 165 Saddle hyperbolic fixed point 446 Saddle point 53 87 Satellite (prob) 200 scalar 333—334 Scalar potential 525 534 Scalar product 254 334 523 Scaling function, universal See universal scaling function Scaling transformation 487 Scattering angle 152 Schrodinger equation 229 384 67 Scleronomic constraints See constraints scleronomic Second-order differential equation See differential equation second-order Secular terms 400 404—405 Self-similarity 487—488 Semi-axes 306 Semimajor axes 472 Semimajor axes, ellipse 145—146 Semiminor axis, ellipse 145—146 Separability 208 225—226 Separation constants 221 Separation constants of variables 221 228 Separatrix 128 185 232 435 442 Sgrad 236 SHO See oscillator simple SI units 507 540 Similarity transformation 487 Simultaneity 494 500 501—503 Simultaneous rotations 258 Sinelike 390 Skew gradient 236 SLAC 536 Sleeping top 316 Small oscillations, theory of 343—371 373—374 Small vibrations See small oscillations Small-angle approximation 349 Snell's Law (prob) 71 Solar system, stability 424 468—474 Solenoid lens for electrons (prob) 199 Southern cross 317 Space cone 297 298 Space cone, coordinate system 259—264 284 300 Space-time areas, diagrams 495—498 501—503 Space-time areas, event 521 Space-time areas, transformation of 501 Spacelike separation 522 Special relativity 493—540 [542 546—548 550 553] Special relativity, two postulates 494 speed of light 494 Spherical pendulum 27 (prob) Spherical pendulum, Hamiltonian 183—184 Spin 293 296—297 313 Spin of electron in magnetic field (prob) 277 Spring pendulum (prob) 27 Square pulse 100—101 104 Stability 392 413—114 Stability, matrix 443—446 449 458 485 Stability, matrix, dynamical 383 386 Stability, matrix, marginal 474 Stability, matrix, of many-dimensional Linear systems near equilibrium 359—360 Stability, matrix, solar system See solar system stability Stable equilibrium See equilibrium stable Stable equilibrium, fixed point See fixed point stable Stable equilibrium, manifold, See manifold stable Staeckel conditions 226 Standard map (prob) 476 Standing waves on a string 371 State vector 330 355 357 Stationary action, path for 53 Steady-state solution See oscillator steady-state Stellar aberration (prob) 553 Step function 96—97 Stoke's theorem 231 Strange attractar 425 453 461—463 Subharmonic oscillations 383 409—41L Successive approximations method of 270—271 Summation convention for indices 253 Supercycle 484 486—487 Superposition 89 344 120 Superstable fixed point See fixed point superstable Surface of section See Poincare' section Sussman, G.L. 471—472 Swing See pumping a swing (prob) Symmetric matrices, diagonalization 336—339 Symmetric matrices, rotational kinetic energy 305 Symmetric matrices, top 289 Symmetric matrices, top, heavy 284 313—317 331 Symmetric matrices, top, Lagrangian 313 Symmetric matrices, torque free 293—300 374 Symmetry breaking 455—456 Symplectic 248—251 431—432 Tachyons (prob) 544 Tangent map See stability matrix Taylor series 482 Taylor series, expansion 24 47—48 83—84 128 Tensor 286 333—336 Tensor, first-rank 333—334 Tensor, inertia See inertia tensor Tensor, second-rank 286 319 333—336 Tensor, zero-rank 333—334 Tether ball (prob) 162 Three-body problem 226—235 Three-body problem, restricted (prob) 478 Three-dimensional rotations See rotations three-dimensional Tides 322 163 Time derivative, transformation of coordinate systems 266 Time derivative, vector See vector time Time dilation 499—500 543 Timelike separation 521—522 Tippe top (prob) 331 Top See symmetric top asymmetric topology 235 Tori, KAM See KAM tori Torus 235 429 See Tower of Pisa problem 253 267—271 Trace 204 303 392 445 Transformation law, electric and magnetic forces 508—510 Transformation law, electric field for light pulse 510—511 Transformation law, energy of light wave 507—512 Transformation law, frequency of light wave 505—507 Transformation law, Galilean See Galilean transformation laws Transformation law, volume 511—512 Transformation of coordinates 173 Transformation, canonical See canonical transformations Transformation, contact See contact transformation Transformation, continuous 171 Transformation, discrete 171 Transformation, identity 171 215 Transformation, invariance 174 Transformation, Lorentz See Lorentz transformation Transformation, matrix See matrix transformation Transformation, orthogonal See orthogonal transformation Transformation, point See point transformation Transformation, principal axis See principal axis transformation Transformation, scaling See scaling transformation Transformation, similarity See similarity transformation Transformation, velocity See velocity transformation rules Transient solution See oscillator transient Translation angular momentum See angular momentum translation Translation invariance See invariance translation Translation kinetic energy See kinetic energy translational TRANSPOSE 249—250 262 Transverse momentum, relativistic See momentum transverse nelotivistic Tremaine, S. 471 Triatomic molecule, linear 360—363 377 Triple pendulum (prob) 373 True anomaly 148 Tune 445 Turning point 125 Turntable (prob) 279 Twin paradox 534—557 Two-body problem 134 Uncountable 465 Underdamped See oscillator damped Unitary matrix 263 Universal scaling function 488—490 Unprimed frame 260 Unstable equilibrium See equilibrium stable Unstable fixed point See fixed point unstable Unstable manifold See manifold unstable Unstable motion See instability Upside-down pendulum 397—398 415 Van der Pol equation (prob) 420 Variation 47 Variation in the integral I 48 Variation principle 54—55 Variational calculus 44 51 Variational calculus, derivative 53 Variational calculus, principle 532—533 Variational calculus, shortest distance between two points 49—50 Varied curve 47 Vector 253—254 333—334 Vector field 235 Vector potential 525 534 538 Vector, time derivative 253 Vectorial mechanics 23 Velocity, generalized See generalized velocity Velocity, relativistic 504—505 542 Velocity, transformation of coordinate systems 264—265 Velocity, transformation rules 0 Venus See solar system stability Vibrational state, complex See state vector Vibrations, small See small oscillations Virtual displacement 4—5 14—15 Virtual work 4—5 9 14—15 27 Voltaire 75 340 Volume, transformation law See transformation law volume Voyager 163 Water molecule (prob) 375 Wave equation 371 Wave vector 526 Weber 493 Whittaker, E.T. 293 308—309 Width, full at half max 109 Wigner, E.P. 44 Winding number 237—239 425 427—432 434 461 Winding number, irrational 238—239 436—437 Winding number, rational 238—239 Wisdom, J. 469—472 WKB limit 230 Work, definition of 4—5 World line 496 531 Wren, Sir Christopher 132 WWI. Falkland Islands battle (prob) See Falkland Islands battle (prob)
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