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ОбложкаMorin D. Introduction to classical mechanics: with problems and solutions. - Cambridge; New York: Cambridge University Press, 2008. - xvii, 719 p. - Ref.: p.713-715. - Ind.: p.713-719. - ISBN 978-0-521-87622-3
Шифр: (И/В2-М84) 02
 

Место хранения: 02 | Отделение ГПНТБ СО РАН | Новосибирск

Оглавление / Contents
 
 
Preface ...................................................... xiii

1  Strategies for solving problems .............................. 1
   1.1  General strategies ...................................... 1
   1.2  Units, dimensional analysis ............................. 4
   1.3  Approximations, limiting cases .......................... 7
   1.4  Solving differential equations numerically ............. 11
   1.5  Problems ............................................... 14
   1.6  Exercises .............................................. 15
   1.7  Solutions .............................................. 18

2  Statics ..................................................... 22
   2.1  Balancing forces ....................................... 22
   2.2  Balancing torques ...................................... 27
   2.3  Problems ............................................... 30
   2.4  Exercises .............................................. 35
   2.5  Solutions .............................................. 39

3  Using F = ma ................................................ 51
   3.1  Newton's laws .......................................... 51
   3.2  Free-body diagrams ..................................... 55
   3.3  Solving differential equations ......................... 60
   3.4  Projectile motion ...................................... 65
   3.5  Motion in a plane, polar coordinates ................... 68
   3.6  Problems ............................................... 70
   3.7  Exercises .............................................. 75
   3.8  Solutions .............................................. 84

4  Oscillations ............................................... 101
   4.1  Linear differential equations ......................... 101
   4.2  Simple harmonic motion ................................ 105
   4.3  Damped harmonic motion ................................ 107
   4.4  Driven (and damped) harmonic motion ................... 109
   4.5  Coupled oscillators ................................... 115
   4.6  Problems .............................................. 120
   4.7  Exercises ............................................. 122
   4.8  Solutions ............................................. 127

5  Conservation of energy and momentum ........................ 138
   5.1  Conservation of energy in one dimension ............... 138
   5.2  Small oscillations .................................... 147
   5.3  Conservation of energy in three dimensions ............ 148
   5.4  Gravity ............................................... 152
   5.5  Momentum .............................................. 156
   5.6  The center of mass frame .............................. 161
   5.7  Collisions ............................................ 164
   5.8  Inherently inelastic processes ........................ 167
   5.9  Problems .............................................. 173
   5.10 Exercises ............................................. 180
   5.11 Solutions ............................................. 194

6  The Lagrangian method ...................................... 218
   6.1  The Euler-Lagrange equations .......................... 218
   6.2  The principle of stationary action .................... 221
   6.3  Forces of constraint .................................. 227
   6.4  Change of coordinates ................................. 229
   6.5  Conservation laws ..................................... 232
   6.6  Noether's theorem ..................................... 236
   6.7  Small oscillations .................................... 239
   6.8  Other applications .................................... 242
   6.9  Problems .............................................. 246
   6.10 Exercises ............................................. 251
   6.11 Solutions ............................................. 255

7  Central forces ............................................. 281
   7.1  Conservation of angular momentum ...................... 281
   7.2  The effective potential ............................... 283
   7.3  Solving the equations of motion ....................... 285
   7.4  Gravity, Kepler's laws ................................ 287
   7.5  Problems .............................................. 296
   7.6  Exercises ............................................. 298
   7.7  Solutions ............................................. 300

8  Angular momentum, Part I (Constant fig.3) ...................... 309
   8.1  Pancake object in x-y plane ........................... 310
   8.2  Nonplanar objects ..................................... 316
   8.3  Calculating moments of inertia ........................ 318
   8.4  Torque ................................................ 322
   8.5  Collisions ............................................ 328
   8.6  Angular impulse ....................................... 331
   8.7  Problems .............................................. 333
   8.8  Exercises ............................................. 339
   8.9  Solutions ............................................. 349

9  Angular momentum, Part II (General fig.3) ...................... 371
   9.1  Preliminaries concerning rotations .................... 371
   9.2  The inertia tensor .................................... 376
   9.3  Principal axes ........................................ 383
   9.4  Two basic types of problems ........................... 388
   9.5  Euler's equations ..................................... 393
   9.6  Free symmetric top .................................... 396
   9.7  Heavy symmetric top ................................... 399
   9.8  Problems .............................................. 415
   9.9  Exercises ............................................. 421
   9.10 Solutions ............................................. 428

10 Accelerating frames of reference ........................... 457
   10.1 Relating the coordinates .............................. 458
   10.2 The fictitious forces ................................. 460
   10.3 Tides ................................................. 471
   10.4 Problems .............................................. 477
   10.5 Exercises ............................................. 482
   10.6 Solutions ............................................. 486

11 Relativity (Kinematics) .................................... 501
   11.1 Motivation ............................................ 502
   11.2 The postulates ........................................ 509
   11.3 The fundamental effects ............................... 511
   11.4 The Lorentz transformations ........................... 523
   11.5 Velocity addition ..................................... 529
   11.6 The invariant interval ................................ 533
   11.7 Minkowski diagrams .................................... 536
   11.8 The Doppler effect .................................... 539
   11.9 Rapidity .............................................. 543
   11.10 Relativity without с ................................. 546
   11.11 Problems ............................................. 549
   11.12 Exercises ............................................ 556
   11.13 Solutions ............................................ 565

12 Relativity (Dynamics) ...................................... 584
   12.1 Energy and momentum ................................... 584
   12.2 Transformations of E and p ............................ 594
   12.3 Collisions and decays ................................. 596
   12.4 Particle-physics units ................................ 600
   12.5 Force ................................................. 601
   12.6 Rocket motion ......................................... 606
   12.7 Relativistic strings .................................. 609
   12.8 Problems .............................................. 611
   12.9 Exercises ............................................. 615
   12.10 Solutions ............................................ 619

13 4-vectors .................................................. 634
   13.1 Definition of 4-vectors ............................... 634
   13.2 Examples of 4-vectors ................................. 635
   13.3 Properties of 4-vectors ............................... 637
   13.4 Energy, momentum ...................................... 639
   13.5 Force and acceleration ................................ 640
   13.6 The form of physical laws ............................. 643
   13.7 Problems .............................................. 645
   13.8 Exercises ............................................. 645
   13.9 Solutions ............................................. 646

14 General Relativity ......................................... 649
   14.1 The Equivalence Principle ............................. 649
   14.2 Time dilation ......................................... 650
   14.3 Uniformly accelerating frame .......................... 653
   14.4 Maximal-proper-time principle ......................... 656
   14.5 Twin paradox revisited ................................ 658
   14.6 Problems .............................................. 660
   14.7 Exercises ............................................. 663
   14.8 Solutions ............................................. 666

Appendix A  Useful formulas ................................... 675
Appendix В  Multivariable, vector calculus .................... 679
Appendix C  F = ma vs. F= dp/dt ............................... 690
Appendix D  Existence of principal axes ....................... 693
Appendix E  Diagonalizing matrices ............................ 696
Appendix F  Qualitative relativity questions .................. 698
Appendix G  Derivations of the Lν/c2 result ................... 704
Appendix H  Resolutions to the twin paradox ................... 706
Appendix I  Lorentz transformations ........................... 708
Appendix J  Physical constants and data ....................... 711
References .................................................... 713
Index ......................................................... 716

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