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Hand L.N., Finch J.D. Ч Analytical Mechanics
Hand L.N., Finch J.D. Ч Analytical Mechanics

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Ќазвание: Analytical Mechanics

јвторы: Hand L.N., Finch J.D.


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: en

–убрика: ‘изика/ лассическа€ физика/“еоретическа€ механика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1998

 оличество страниц: 574

ƒобавлена в каталог: 19.06.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
ѕредметный указатель
Accelerated systems, Hamiltonian dynamics      See Hamiltonian dynamics in
Acceleration and relation to mass      512Ч513
Acceleration block on inclined plane      2Ч3
Acceleration caused by a constant fame      535Ч536
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      230Ч231
Action-angle variables      230Ч235 237 238 246Ч247
Action-angle variables, pendulum      See pendulum action-angle
Adiabatic invariants      118 233Ч235
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      137Ч139 170Ч172 283 245
Angular momentum barrier      140Ч141
Angular momentum, intrinsic      See angular momentum rotational
Angular momentum, rotational      292
Angular momentum, total      291Ч292
Angular momentum, translational      292
Angular velocity      256Ч257 264Ч266 283 293 304 306 276Ч277
Anharmonic oscillator      398Ч401
Anharmonic oscillator, driven      401Ч411
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      383Ч411
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      167Ч169
Asymmetric top      288 331
Asymmetric top, kinetic energy      306
Asymmetric top, torque free      305Ч312
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      44Ч46 344
Bertrand's theorem      154
Bertrand's theorem (prob)      167
Bicycle (prob)      27
Bifurcation diagrams      459Ч460 484Ч485 491
Bifurcation diagrams, pitchfork      459 483Ч484 486
big bang      325 456
Binding energy      5)6
Biot Ч Savart law      509
Birkhoff      439 (see also Poincare Ч Birkhoff theorem)
Black body radiation      325
Black hole M87      155
Block on inclined plane, example      1Ч7
Body cone      297 298
Body coordinate system      259Ч264 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      38Ч39 35
Box-Counting Dimension      See dimension box-counting
Brachistochrone      44Ч46 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      190Ч192
Butterfly effect      425
Calculus of variations      See variational calculus
Campion generator (prob)      280
Canonical transformations      207Ч213 215Ч218 237 250 24l-244
Canonically conjugate momentum      22 75 170 172 175 181 538 34Ч35
Canonnball example      52 77
Cantor set      464Ч468
Capacitor (prob)      116
Capacity dimension      See dimension box-counting
Catenary curve      62
Cattini      339Ч440
Causal Green's function      See Green's function causal
Cavity, cylindrical      See gedanken experiment cylindrical
Center of mass      134 136Ч137
Center of momentum      See center of mass
Center of motion      283 285 292 298 160Ч161
Central force      24 133Ч141 [161Ч162 198 413] see
Central motion, effective potential      140Ч141
Central motion, energy diagram      142
Central motion, Kepler's Laws      132 139
Central motion, orbit equation      142Ч143
Central motion, stability of circular orbit      384Ч388
Centrifugal force      142 267
centripetal acceleration      40
CERES      148
cgs units      507 540
Chain example      61
Chain rule      6
Chandler wobble      299Ч300
Chandler, S.      300
Chaos      237 475
Chaos in conservative systems      379 425 428Ч452 472
Chaos in dissipative systems      425 452Ч468
Chaotic dynamics      423Ч474
Characteristic exponent      391
Characteristic multiplier      444
Characteristic polynomial      337
Charge conservation      188
Circular hoop with 3 point masses connected by massless springs      365Ч367
Circular motion, relativistic      See relativistic circular motion
Circular orbits      144 385
Classically forbidden      126
Clockwork universe      423
Coastline      See dimension of
Cofactors      355 362 380Ч382
Comets (prob)      163
complex numbers      111
Complex solutions      89
Compton scattering (prob)      549
Compton, A.H.      252 280
Configuration space      36Ч37 229
Conic section      144
Conjugate momentum      See canonically conjugate momentum
Conservation of angular momentum      170Ч172
Conservation of charge      See charge conservation
Conservation of energy, relativistic (prob)      547
Conservation of momentum      See momentum conservation
Conservative forces      18 41Ч43
Conserved function      11
Conserved quantity      174
Constant of the motion      21 22 138 170 172 196
Constraint force      2 57
Constraint force, generalized      60Ч61
Constraints      12Ч13
Constraints, holonomic      13 57Ч5S 83 85 33
Constraints, nonholonomic      36Ч40 62Ч64 35
Constraints, nonintegrable      36
Constraints, rheonomic      13 22
Constraints, scleronomic      13 22 85
Contact transformation      208 211
Continued fraction expansion      436Ч437
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 24Ч25
Coordinate system, polar, elliptical      309Ч310
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      130Ч131
Coriolis force      267
Cosinelike      390
Cosmic rays      537
Coulomb potential      See hyperbolic orbits repulsive
Coupled pendulum      See pendulum two
Covariant components      529
Covariant procedure      538Ч539
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      85Ч86
Cyclic coordinates      See ignorable coordinates
Cyclotron frequency, relativistic      540
D'Alembert      4 322
D'Alembert's principle      5
Damped driven pendulum      425 453Ч463 467Ч468
Damped oscillator      See oscillattor damped
Dark matter      154Ч156
Day, length of in age of dinosaurs (prob)      282
Degeneracy      339 343 353
Degeneracy modes      365Ч367
Degrees of freedom      2 8 10Ч12 36 86 27
Degrees of freedom, relational      283
Delta function      99Ч100
Derivative, directional      See directional derivative
Derivative, Lie      See Lie derivative
Determinant      203 352
Deterministic chaos      424
Diagonalization      392
Diagonalization of symmetric matrices      336Ч339
Diagonalization of t and v matrices      364Ч365
Diatomic molecule (prob)      377
Diffeomorphism      55
Differential equation, linear, inhomogeneous      95
Differential equation, linear, ordinary, second-order, and homogeneous      88Ч89
Differential equation, linear, superposition      88Ч89
Differential equation, second order      24
Differential equations of motion      See equations of motion
DIMENSION      463Ч468
Dimension, box counting      463Ч466
Dimension, fractional      463Ч464 see
Dimension, Hausdorff      463
Dimension, Lyapunov      467
Dimension, magnification      466
Dimension, of coastline of Britain      465Ч466
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      101Ч102
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 426Ч428 430Ч433 435 440Ч442 451Ч452
Double pendulum, Hamiltonian      426Ч427
Double pendulum, Lagrangian      549
Double pendulum, small angle approximation      348Ч355 358Ч359 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 398Ч401 [158 419]
Duffing oscillator, driven      401Ч411
Duffing oscillator, period of      401
Dumbbell, inertia tensor      290Ч291
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      267Ч275
Earth, equatorial bulge      See equatorial bulge
Eccentric anomaly      148Ч150
Eccentricity      323 470Ч473
Eccentricity, ellipse      144
Effective potential      140Ч142 385
Eigenvalues      302Ч303 336Ч339 392 444 449
Eigenvalues, generalized      353 359
Eigenvectors      302Ч303 337Ч339 392 444 449
Eigenvectors, generalized      353
Einstein summation convention      253 529
Einstein, A.      154 493Ч495 508 514 516 519 533
Electric and magnetic field, antisymmetric four-tensor      See antisymmetric four-tensor electric
electric field      493 508Ч510 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)      199Ч200 550 551
Electromagnetic field, relativistic Lagrangian      See relativistic Lagrangian electromagnetic
Electron capture      135
Electron-positron annihilation      517
Electrostatics (prob)      67
Elevator      20 200
ellipse      144Ч145
Ellipse, aphelion      145
Ellipse, apsides      145
Ellipse, eccentricity      144
Ellipse, perihelion      145
Ellipse, semimajor axis      145Ч146
Ellipse, semiminor axis      145Ч146
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      145Ч147
Elliptical motion, time dependence      147Ч150
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      515Ч517 533
Energy, stored in oscillator      See oscillator stored
1 2 3 4
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