Structure and Interpretation of Classical Mechanics > 물리학

Lagrangian Mechanics p. 1
The Principle of Stationary Action p. 4
Configuration Spaces p. 9
Generalized Coordinates p. 11
Computing Actions p. 16
The Euler-Lagrange Equations p. 26
How to Find Lagrangians p. 37
Evolution of Dynamical State p. 66
Conserved Quantities p. 74
Abstraction of Path Functions p. 87
Constrained Motion p. 94
Rigid Bodies p. 113
Rotational Kinetic Energy p. 114
Kinematics of Rotation p. 116
Moments of Inertia p. 118
Inertia Tensor p. 121
Principal Moments of Inertia p. 122
Representation of the Angular Velocity Vector p. 125
Euler Angles p. 128
Vector Angular Momentum p. 132
Motion of a Free Rigid Body p. 134
Axisymmetric Tops p. 143
Spin-Orbit Coupling p. 151
Euler\'s Equations p. 163
Nonsingular Generalized Coordinates p. 168
Hamiltonian Mechanics p. 179
Hamilton\'s Equations p. 181
Poisson Brackets p. 203
One Degree of Freedom p. 206
Phase Space Reduction p. 208
Phase Space Evolution p. 220
Surfaces of Section p. 223
Exponential Divergence p. 247
Liouville\'s Theorem p. 250
Standard Map p. 260
Phase Space Structure p. 267
Emergence of the Divided Phase Space p. 268
Linear Stability p. 273
Homoclinic Tangle p. 284
Integrable Systems p. 292
Poincare-Birkhoff Theorem p. 297
Invariant Curves p. 303
Canonical Transformations p. 319
Point Transformations p. 320
General Canonical Transformations p. 324
Invariants of Canonical Transformations p. 339
Extended Phase Space p. 346
Reduced Phase Space p. 355
Generating Functions p. 359
Time Evolution Is Canonical p. 391
Hamilton-Jacobi Equation p. 403
Lie Transforms p. 417
Lie Series p. 423
Exponential Identities p. 431
Canonical Perturbation Theory p. 439
Perturbation Theory with Lie Series p. 440
Pendulum as a Perturbed Rotor p. 442
Many Degrees of Freedom p. 455
Nonlinear Resonance p. 459
Appendix: Scheme p. 479
Appendix: Our Notation p. 489
References p. 505
List of Exercises p. 509
Index p. 511