Lecture 7. Examples of Hamiltonian Systems. Liouville-Arnold Integrability

  1. 00:16Definition From the Previous Lecture: Generic Symplectic Leaf
  2. 03:29Homework: Problem 1 (Prove the Formula: Poisson Bracket and Differential Form)
  3. 04:43Casimir Functions and Degenerate Poisson Bivectors. Generic Symplectic Leaf
  4. 15:28Examples of Hamiltonian Systems. Example 1: The Kepler Problem
  5. 41:15Homework: Problem 2 (In Kepler Problem, Find a Family of 3 Independent Integrals in Involution)
  6. 54:05Examples of Hamiltonian Systems. Example 2: The Euler Top
  7. 01:04:59Homework: Problem 3 (Lemma: Euler Top is a Hamiltonian System)
  8. 01:06:53Liouville-Arnold Integrability
  9. 01:13:29Theorem (Liouville-Arnold): Formulation