Талалаев Д.В. - Algebraic Structures in Integrable Systems - 7. Examples of Hamiltonian Systems

Описание

Examples of Hamiltonian Systems. Liouville-Arnold Integrability
Талалаев Дмитрий Валерьевич

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

Ссылка на плейлист Teach-In: https://teach-in.ru/course/algebraic-structures-in-integrable-systems
Ссылка на плейлист YouTube: https://www.youtube.com/playlist?list=PLcsjsqLLSfNC7GTTCsKar-GSTZkkN22oA
Ссылка на плейлист VK: https://vkvideo.ru/playlist/-176441665_824
Ссылка на плейлист RuTube: https://rutube.ru/plst/1213198

#teach_in #мгу #msu #итмф #itmp #лекции #lectures #Талалаев #Talalaev #algebraic_structures #integrable_systems #Hamiltonian_dynamics #Poisson_structure #Poisson_bivector #Poisson_bracket #symplectic_structure #Hamiltonian_fector_fields #generic_symplectic_leaf #integrals_of_motion #Casimir_functions #Kepler_problem #Euler_top #Liouville_Arnold_integrability #Liouville_Arnold_theorem