幾何力學     [Geometric Mechanics 1]   [Geometric Mechanics 2]   [幾何分析]   [辛幾何]

[黎曼幾何及其在力學與相對論的應用]      [GM01]第五章

Leonor Godinho         Jose Natario

1. 力學系統   [為什麼要研究動力系統]      伽利略  牛頓1687   海王星(Neptune)1846   天王星(Uranus)
2. 可積約束(holonomic constrains)---(1)滾動之輪  (2)單擺
3. rigid body
4. 非可積約束---(1)溜冰
5. Lagrange力學 [Euler-Lagrange equations]---這裡有一個解速降線微分方程的解法
6. Hamilton力學---[Hamilton equations] [symplectic forms] [Poisson bracket]      symplectic and Poisson manifolds
7. completely integrable systems
8. Symmetry and Reduction

Jacobi metric

Noether theorem conservation laws to symmetry

Darryl D Holm

[Geometric Mechanics] Part I : Dynamics and Symmetry      Darryl D Holm

[Geometric Mechanics]

[GeometricMechanics] Part II

[幾何力學]  

  [Journal of Geometric Mechanics]

Manuel de Leon      Andrew Lewis      Juan-Pablo Ortega

Pawel Urbanski