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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
Accelerated systems, Hamiltonian dynamics See Hamiltonian dynamics in Acceleration and relation to mass 512—513 Acceleration block on inclined plane 2—3 Acceleration caused by a constant fame 535—536 Acceleration elevator 20 Acceleration transformation of coordinate systems 266 Action functional S 51 178 220 Action principle See variation: principle Action principle, extended See extended action Action principle, relativist See relativist action Action principle, variable 230—231 Action-angle variables 230—235 237 238 246—247 Action-angle variables, pendulum See pendulum action-angle Adiabatic invariants 118 233—235 Airplane wings 397 Almagest 130 Almost periodic 238 Amplifiers, parametric See parametric amplifiers Analytical mechanics 23 Angle variably 230 232 Angular frequency 526 Angular momentum barrier 140—141 Angular momentum, intrinsic See angular momentum rotational Angular momentum, rotational 292 Angular momentum, total 291—292 Angular momentum, translational 292 Angular velocity 256—257 264—266 283 293 304 306 276—277 Anharmonic oscillator 398—401 Anharmonic oscillator, driven 401—411 Anharmonic oscillator, period of 401 Annihilation radiation 517 Antisymmetric four-tensor, electric and magnetic fields 530 539 Antisymmetric matrix 264 304 Aphelion, ellipse See ellipse aphelion Apparent force 267 Approximate solutions to non-analytic problems 383—411 Apsides, ellipse See ellipse apsides Arc length 138 Area-preserving map See map area-preserving Arisiarchus of Santos 317 Aristotle 317 Arnold See KAM theorem Arnold diffusion 451 470 472 Asteroid belt 469 Asteroid, perturbed by Jupiter (prob) 417 Astrophysical data, table of 167—169 Asymmetric top 288 331 Asymmetric top, kinetic energy 306 Asymmetric top, torque free 305—312 Attractive force, hyperbolic orbits See hyperbolic orbits attractive Attractor 452 (see also phase space trajectories) Attractor, periodic 425 Attractor, strange See strange attractor Atwood machine, double (prob) 31 Axial vector See pseudovector Axions 155 Band theory, of solids 390 Basins of attraction 453 Bead on wire (prob) 30 34 114 Beam stability 390 Beat frequency See frequency beat Bernoulli, Daniel 45 86 344 Bernoulli, Jacques 4 Bernoulli, Jean 44—46 344 Bertrand's theorem 154 Bertrand's theorem (prob) 167 Bicycle (prob) 27 Bifurcation diagrams 459—460 484—485 491 Bifurcation diagrams, pitchfork 459 483—484 486 big bang 325 456 Binding energy 5)6 Biot — Savart law 509 Birkhoff 439 (see also Poincare — Birkhoff theorem) Black body radiation 325 Black hole M87 155 Block on inclined plane, example 1—7 Body cone 297 298 Body coordinate system 259—264 284 300 Boldface notation 262 Boost See Lorentz transformations Bouncing bull (prob) 475 Boundary conditions, matching See matching boundary conditions Boundary curve for Poincare section of double pendulum 431 Bowling ball 38—39 35 Box-Counting Dimension See dimension box-counting Brachistochrone 44—46 70 Brahe, Tycho 131 Britain, dimension of coastline See dimension of coastline of Britain Broken symmetry See symmetry breaking Brown dwarfs 155 Bug crawling on a phonograph turntable, Hamiltonian and Lagrangian 190—192 Butterfly effect 425 Calculus of variations See variational calculus Campion generator (prob) 280 Canonical transformations 207—213 215—218 237 250 24l-244 Canonically conjugate momentum 22 75 170 172 175 181 538 34—35 Canonnball example 52 77 Cantor set 464—468 Capacitor (prob) 116 Capacity dimension See dimension box-counting Catenary curve 62 Cattini 339—440 Causal Green's function See Green's function causal Cavity, cylindrical See gedanken experiment cylindrical Center of mass 134 136—137 Center of momentum See center of mass Center of motion 283 285 292 298 160—161 Central force 24 133—141 [161—162 198 413] see Central motion, effective potential 140—141 Central motion, energy diagram 142 Central motion, Kepler's Laws 132 139 Central motion, orbit equation 142—143 Central motion, stability of circular orbit 384—388 Centrifugal force 142 267 centripetal acceleration 40 CERES 148 cgs units 507 540 Chain example 61 Chain rule 6 Chandler wobble 299—300 Chandler, S. 300 Chaos 237 475 Chaos in conservative systems 379 425 428—452 472 Chaos in dissipative systems 425 452—468 Chaotic dynamics 423—474 Characteristic exponent 391 Characteristic multiplier 444 Characteristic polynomial 337 Charge conservation 188 Circular hoop with 3 point masses connected by massless springs 365—367 Circular motion, relativistic See relativistic circular motion Circular orbits 144 385 Classically forbidden 126 Clockwork universe 423 Coastline See dimension of Cofactors 355 362 380—382 Comets (prob) 163 complex numbers 111 Complex solutions 89 Compton scattering (prob) 549 Compton, A.H. 252 280 Configuration space 36—37 229 Conic section 144 Conjugate momentum See canonically conjugate momentum Conservation of angular momentum 170—172 Conservation of charge See charge conservation Conservation of energy, relativistic (prob) 547 Conservation of momentum See momentum conservation Conservative forces 18 41—43 Conserved function 11 Conserved quantity 174 Constant of the motion 21 22 138 170 172 196 Constraint force 2 57 Constraint force, generalized 60—61 Constraints 12—13 Constraints, holonomic 13 57—5S 83 85 33 Constraints, nonholonomic 36—40 62—64 35 Constraints, nonintegrable 36 Constraints, rheonomic 13 22 Constraints, scleronomic 13 22 85 Contact transformation 208 211 Continued fraction expansion 436—437 Continuity equation 188 525 Continuous transformations See transformations continuous Contravariant components 529 Control parameter 481 Coordinate system, body See body coordinate system Coordinate system, polar, cylindrical 10 19 24—25 Coordinate system, polar, elliptical 309—310 Coordinate system, polar, spherical 10 51 138 226 Coordinate system, rotating See rotating reference frames Coordinate system, space See space coordinate system Coordinates, generalized See generalized coordinates Copernicus, Nicolaus 130—131 Coriolis force 267 Cosinelike 390 Cosmic rays 537 Coulomb potential See hyperbolic orbits repulsive Coupled pendulum See pendulum two Covariant components 529 Covariant procedure 538—539 Cramer's rule 380 Critical damping (prob) 117 121 Critically damped See oscillator damped Cross section (prob) 165 Cubic polynomials 315 Curvature, of potential energy 85—86 Cyclic coordinates See ignorable coordinates Cyclotron frequency, relativistic 540 D'Alembert 4 322 D'Alembert's principle 5 Damped driven pendulum 425 453—463 467—468 Damped oscillator See oscillattor damped Dark matter 154—156 Day, length of in age of dinosaurs (prob) 282 Degeneracy 339 343 353 Degeneracy modes 365—367 Degrees of freedom 2 8 10—12 36 86 27 Degrees of freedom, relational 283 Delta function 99—100 Derivative, directional See directional derivative Derivative, Lie See Lie derivative Determinant 203 352 Deterministic chaos 424 Diagonalization 392 Diagonalization of symmetric matrices 336—339 Diagonalization of t and v matrices 364—365 Diatomic molecule (prob) 377 Diffeomorphism 55 Differential equation, linear, inhomogeneous 95 Differential equation, linear, ordinary, second-order, and homogeneous 88—89 Differential equation, linear, superposition 88—89 Differential equation, second order 24 Differential equations of motion See equations of motion DIMENSION 463—468 Dimension, box counting 463—466 Dimension, fractional 463—464 see Dimension, Hausdorff 463 Dimension, Lyapunov 467 Dimension, magnification 466 Dimension, of coastline of Britain 465—466 Dimension, of strange attractor of damped driven pendulum 468 Dirac delta function See delta function Dirac, P.A.M. 44 Directional derivative 236 Discontinuity, in Green's function 101—102 Discrete transformations See transformations discrete Displaced axis theorem 289 Displacement ratio See mode displacement ratio Dissipative flow 189 Divergence 192 Divergence, exponential of trajectories See characteristic exponent Doppler shift 505 507 515 546 Dot cancellation 14 Dot product See scalar product Double pendulum, exact 425 426—428 430—433 435 440—442 451—452 Double pendulum, Hamiltonian 426—427 Double pendulum, Lagrangian 549 Double pendulum, small angle approximation 348—355 358—359 377 Double-well potential (prob) 157 Driven oscillator See oscillator driven Driven support of pendulum See pendulum with DSHO See oscillator dumped Duffing oscillator 384 398—401 [158 419] Duffing oscillator, driven 401—411 Duffing oscillator, period of 401 Dumbbell, inertia tensor 290—291 Dynamical equilibrium See equilibrium dynamical Dynamical equilibrium, instability See instability dynamical Dynamical equilibrium, stability See stability dynamical Dynamical equilibrium, variable 7 Earth See solar system stability Earth as noninertial reference frame 267—275 Earth, equatorial bulge See equatorial bulge Eccentric anomaly 148—150 Eccentricity 323 470—473 Eccentricity, ellipse 144 Effective potential 140—142 385 Eigenvalues 302—303 336—339 392 444 449 Eigenvalues, generalized 353 359 Eigenvectors 302—303 337—339 392 444 449 Eigenvectors, generalized 353 Einstein summation convention 253 529 Einstein, A. 154 493—495 508 514 516 519 533 Electric and magnetic field, antisymmetric four-tensor See antisymmetric four-tensor electric electric field 493 508—510 522 Electric field, charged particle See particle in electric and magnetic fields Electric field, transformation law for light pulse See transformation law electric Electric force, transformation law See transformation law electric Electromagnetic field (prob) 199—200 550 551 Electromagnetic field, relativistic Lagrangian See relativistic Lagrangian electromagnetic Electron capture 135 Electron-positron annihilation 517 Electrostatics (prob) 67 Elevator 20 200 ellipse 144—145 Ellipse, aphelion 145 Ellipse, apsides 145 Ellipse, eccentricity 144 Ellipse, perihelion 145 Ellipse, semimajor axis 145—146 Ellipse, semiminor axis 145—146 Ellipsoid, equation of 306 Ellipsoid, inertia 306 Ellipsoid, inertia tensor (prob) 327 Ellipsoid, momental 306 Ellipsoid, oblate 289 Ellipsoid, prolate 289 Elliptic 317 Elliptic fixed points See fixed points elliptic Elliptic orbits 145 385 162 Elliptical motion, period of 145—147 Elliptical motion, time dependence 147—150 Energy 21 (see also Hamiltonian) Energy binding See binding energy Energy momentum four-vector See four-vector energy-momentum Energy of light wave, transformation law See transformation law energy Energy, relativistic 515—517 533 Energy, stored in oscillator See oscillator stored Entrainment (prob) 480
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