经典力学的数学方法
出版时间:
1999-11
版次:
2
ISBN:
9787506200905
定价:
87.00
装帧:
平装
开本:
24开
纸张:
胶版纸
页数:
516页
88人买过
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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
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内容简介:
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.
-
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 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
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