经典力学的数学方法·第2版(英文版)

Many different mathematical methods and concepts are used in classical mechanics: differential equations and phase flows, smooth mappings and manifolds, Lie groups and Lie algebras, symplectic geometry and ergodic theory. Many modern mathematical theories arose from problems in mechanics and only later acquired that axiomatic-abstract form which makes them so hard to study.

Preface
Preface to the second edition
Part I NEWTONIAN MECHANICS
　Chapter 1 Experimental facts
　　1. The principles of relativity and determinacy
　　2. The galilean group and Newton‘s equations
　　3. Examples of mechanical systems
　Chapter 2　Investigation of the equations of motion
　　4. Systems with one degree of freedom
　　5. Systems with two degrees of freedom
　　6. Conservative force fields
　　7. Angular momentum
　　8. Investigation of motion in a central field
　　9. The motion of a point in three-space
　　10. Motions of a system of n points
　　11. The method of similarity
Part II　LAGRANGIAN MECHANICS
　Chapter 3　Variational principles
　　12. Calculus of variations
　　13. Lagrange's equations
　　14. Legendre transformations
　　15. Hamilton's equations
　　16. Liouville's theorem
　Chapter 4　Lagrangian mechanics on manifolds
　　17. Holonomic constraints
　　18. Differentiable manifolds
　　19. Lagrangian dynamical systems
　　20. E. Noether's theorem
　　21. D'Alembert's principle
　Chapter 5　scillations
　　22. Linearization
　　23. Small oscillations
　　24. Behavior of characteristic frequencies
　　25. Parametric resonance
　Chapter 6　Rigid bodies
　　26. Motion in　 a moving coordinate system
　　27. Inertial forces and the Coriolis force
　　28. Rigid bodies
　　29. Euler's equations. Poinsot's description of the motion
　　30. Lagrange's top
　　31. Sleeping tops and fast tops
Part III　HAMILTONIAN MECHANICS
　Chapter 7　Differential forms
　　32. Exterior forms
　　33. Exterior multiplication
　　34. Differential forms
　　35. Integration of differential forms
　　36. Exterior differentiation
　Chapter 8　Symplectic manifolds
　　37. Symplectic structures on manifolds
　　38. Hamiltonian phase flows and their integral invariants6
　　39. The Lie algebra of vector fields
　　40. The Lie algebra of hamiltonian functions
……
Chapter 9 Canonical formalism
Chapter 10 Introduction to perturbation theory
Appendix
Index