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Mathematical Methods of Classical MechanicsPDF|Epub|txt|kindle电子书版本下载
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- ISBN：0387968903
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- 标注页数：508页
- 文件大小：16MB
- 文件页数：522页
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图书目录
Part I NEWTONIAN MECHANICS1
Chapter 1 Experimental facts3
1. The principles of relativity and determinacy3
2. The galilean group and Newton's equations4
3. Examples of mechanical systems11
Chapter 2 Investigation of the equations of motion15
4. Systems with one degree of freedom15
5. Systems with two degrees of freedom22
6. Conservative force fields28
7. Angular momentum30
8. Investigation of motion in a central field33
9. The motion of a point in three-space42
10. Motions of a system of n pomts44
11. The method of similarity50
Part Ⅱ LAGRANGIAN MECHANICS53
Chapter 3 Variational principles55
12. Calculus of variations55
13. Lagrange's equations59
14. Legendre transformations61
15. Hamilton's equations65
16. Liouville's theorem68
Chapter 4 Lagrangian mechanics on manifolds75
17. Holonomic constraints75
18. Differentiable manifolds77
19. Lagrangian dynamical systems83
20. E. Noether's theorem88
21. D'Alembert's principle91
Chapter 5 Oscillations98
22. Linearization98
23. Small oscillations103
24. Behavior of characteristic frequencies110
25. Parametric resonance113
Chapter 6 Rigid Bodies123
26. Motion in a moving coordinate system123
27. Inertial forces and the Coriolis force129
28. Rigid bodies133
29. Euler's equations. Poinsot's description of the motion142
30. Lagrange's top148
31. Sleeping tops and fast tops154
Part Ⅲ HAMILTONIAN MECHANICS161
Chapter 7 Differential forms163
32. Exterior forms163
33. Exterior multiplication170
34. Differential forms174
35. Integration of differential forms181
36. Exterior differentiation188
Chapter 8 Symplectic manifolds201
37. Symplectic structures on manifolds201
38. Hamiltonian phase flows and their integral invariants204
39. The Lie algebra of vector fields208
40. The Lie algebra of hamiltonian functions214
41. Symplectic geometry219
42. Parametric resonance in systems with many degrees of freedom225
43. A symplectic atlas229
Chapter 9 Canonical formalism233
44. The integral invariant of Poincare-Cartan233
45. Applications of the integral invariant of Poincare-Cartan240
46. Huygens' principle248
47. The Hamilton-Jacobi method for integrating Hamilton's canonical equations258
48. Generating functions266
Chapter 10 Introduction to perturbation theory271
49. Integrable systems271
50. Action-angle variables279
51. Averaging285
52. Averaging of perturbations291
Appendix 1 Riemannian curvature301
Appendix 2 Geodesics of left-invariant metrics on Lie groups and the hydrodynamics of ideal fluids318
Appendix 3 Symplectic structures on algebraic manifolds343
Appendix 4 Contact structures349
Appendix 5 Dynamical systems with symmetries371
Appendix 6 Normal forms of quadratic hamiltonians381
Appendix 7 Normal forms of hamiltonian systems near stationary points and closed trajectories385
Appendix 8 Theory of perturbations of conditionally periodic motion, and Kolmogorov's theorem399
Appendix 9 Poincare's geometric theorem, its generalizations and applications416
Appendix 10 Multiplicities of characteristic frequencies, and ellipsoids depending on parameters425
Appendix 11 Short wave asymptotics438
Appendix 12 Lagrangian singularities446
Appendix 13 The Korteweg-de Vries equation453
Appendix 14 Poisson structures456
Appendix 15 On elliptic coordinates469
Appendix 16 Singularities of ray systems480
Index503