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  • 经典力学的数学方法(英文版)[平装]
  • 共3个商家     69.60元~79.17
  • 作者:V.I.Arnold(作者)
  • 出版社:世界图书出版公司北京公司;第2版(1999年11月1日)
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  • ISBN:9787506200905

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    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