从Newton定律到广义Hamiltonian系统(Ⅰ)--关于线性斜对称算子的一些结果

摘要

The Hamiltonian equation provides us an alternative description of the basic physical laws of motion, which is used to be described by Newton's law. The research on Hamiltonian integrable systems is one of the most important topics in the theory of solitons. This article is one of the series of papers regarding the evolution from Newton's law to Hamiltonian system. It demonstrates a necessary and sufficient condition for a linear skew-symmetric operator to be a generalized Hamiltonian. The article aims to provide the readers a good understanding of the development from Newton's laws of motion to integrable Hamiltonian systems and of the physical world.%Newton定律是描述物体运动的基本定律,Hamiltonian方程则为运动的基本规律提供了另外一种表达. 由Hamiltonian方程发展而来的Hamiltonian可积系统是现代孤立子理论的重要组成部分. 本文是介绍从Newton运动定理到Hamiltonian可积系统的演化的系列文章的一部分, 文中证明了一个关于线性斜对称算子为广义Hamiltonian的一个充分和必要条件.