经典力学的数学方法(英文版)
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基本信息·出版社：世界图书出版公司
·页码：518 页
·出版日期：1999年
·ISBN：7506200902
·条形码：9787506200905
·包装版本：2
·装帧：平装
·开本：24开
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内容简介Part ofPreface to the second edition
The main part of this book was written twenty years ago. The ideas and methods of symplectic geometry, developed in this book, have now found many applications in mathematical physics and in other domains of applied mathematics, as well as in pure mathematics itself. Especially, the theory of short wave asymptotic expansions has reached a very sophiscated level, with many important applications to optics, wave theory, acoustics, spectroscopy, and even chemistry; this development was parallel to the development of the theories of Lagrange and Legendre singularities, that is, of singularities of caustics and of wave fronts, of their topology and their perestroikas (in Russian metamorphoses were always called "perestroikas," as in "Morse perestroika" for the English "Morse surgery"; now that the word perestroika has become international, we may preserve the Russian term in translation and are not obliged to substitute "metamorphoses" for "perestroikas" when speaking of wave fronts, caustics, and so on.
目录
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 2Investigation 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 IILAGRANGIAN MECHANICS
Chapter 3Variational principles
12. Calculus of variations
13. Lagrange's equations
14. Legendre transformations
15. Hamilton's equations
16. Liouville's theorem
Chapter 4Lagrangian mechanics on manifolds
17. Holonomic constraints
18. Differentiable manifolds
19. Lagrangian dynamical systems
20. E. Noether's theorem
21. D'Alembert's principle
Chapter 5scillations
22. Linearization
23. Small oscillations
24. Behavior of characteristic frequencies
25. Parametric resonance
Chapter 6Rigid 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 IIIHAMILTONIAN MECHANICS
Chapter 7Differential forms
32. Exterior forms
33. Exterior multiplication
34. Differential forms
35. Integration of differential forms
36. Exterior differentiation
Chapter 8Symplectic 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
……[看更多目录]