- 经典力学的数学方法(第2版影印版)(英文版)
- - 作者：(俄罗斯)V.I.阿诺德
  - 出版社：世界图书出版公司
  - ISBN：9787519255855
  - 出版日期：2019/03/01
  - 页数：516
- 售价：55.6

内容大纲
这是莫斯科大学理论力学的优秀教材，论述了振动理论、刚体运动和哈密顿形式体系等动力学中的所有基本问题，特别强调了边分原理和分析力学及成为量子力学理论基石的哈密顿形式体系。在附录中介绍了经典力学与数学、物理学及其它领域的联系。可供理论力学专业、数学力学专业的研究生及科技人员参考。
作者介绍
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 ofn 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  Oscillations
    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 invariants
    39. The Lie algebra of vector fields
    40. The Lie algebra of hamiltonian functions
    41. Symplectic geometry
    42. Parametric resonance in systems with many degrees of freedom
    43. A symplectic atlas
  Chapter 9  Canonical formalism
    44. The integral invariant of Poincare-Cartan
    45. Applications of the integral invariant of Poincare-Cartan
    46. Huygens' principle
    47. The Hamilton-Jacobi method for integrating Hamilton's canonical equations
    48. Generating functions
  Chapter 10  Introduction to perturbation theory
    49. Integrable systems
    50. Action-angle variables
    51. Averaging
    52. Averaging of perturbations
Appendix 1
  Riemannian curvature
Appendix 2
  Geodesics of left-invariant metrics on Lie groups and the hydrodynamics of ideal fluids
Appendix 3
  Symplectic structures on algebraic manifolds
Appendix 4
  Contact structures
Appendix 5
  Dynamical systems with symmetries
Appendix 6
  Normal forms of quadratic hamiltonians
Appendix 7
  Normal forms of hamiltonian systems near stationary points and closed trajectories
Appendix 8
  Theory of perturbations of conditionally periodic motion, and Kolmogorov's theorem
Appendix 9
  Poincare's geometric theorem, its generalizations and applications
Appendix 10
  Multiplicities of characteristic frequencies, and ellipsoids
  depending on parameters
Appendix 11
  Short wave asymptotics
Appendix 12
  Lagrangian singularities
Appendix 13
  The Korteweg-de Vries equation
Appendix 14
  Poisson structures
Appendix 15
  On elliptic coordinates
Appendix 16
  Singularities of ray systems

Index

内容大纲

作者介绍

目录

同类热销排行榜

推荐书目