经典力学的数学方法(第2版影印版)(英文版)

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。

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