Some Fundamental Techniques in the Theory of Integrable Systems

机译：可积系统理论的几个基本技巧

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The importance of Poisson brackets in classical mechanics was gradually recognized by Lagrange, Poisson and Jacobi. The original remark was as follows: if two mechanical quantities F and G are constants of motion for a certain dynamical system, then a suitable linear combination of products of first-order derivatives of F by similar ones for G, is another constant of motion. We assume that F and G are expressed as functions of positions and velocities of the various parts of the system. In these lectures, we intend to give an introduction to the various aspects of Poisson brackets. Our purpose has been to lay down the differential-geometric foundations for the use of Poisson brackets in the subsequent parts, where the emphasis is on the dynamical systems. Contents: (1) Analytical mechanics and differential geometry; (2) Poisson manifolds and symplectic manifolds; (3) Poisson manifolds and tensor calculus; (4) Symplectic foliations on Poisson manifolds; (5) The momentum map.

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Cartier, P.;
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年度 1994
页码 1-42
总页数 42
原文格式 PDF
正文语种 eng
中图分类工业技术;
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Meetings ; Mathematical manifolds ; Differential equations ; Differential geometry ; Hamiltonian functions ; Lagrangian functions ; Lie algebras ; Dynamical systems ; Classical mechanics ; Tensors;

机译：会议;数学流形;微分方程;微分几何;哈密顿函数;拉格朗日函数;李代数;动力系统;经典力学;张量;

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Some Fundamental Techniques in the Theory of Integrable Systems

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