关于力学变分原理及应用的几点注记

从论述经典力学中的Hamiltonian原理的推广开始，概述泛函分析中算子理论和非平衡热力学变分原理基于场的变分的新发展，余一对偶变分原理集伴随变分法和广义格林函数法于一体，它既是有限元法、又是边界元法最普遍的数学基础；从物理观点看，唯象的非平衡热力学变分原理函盖所有宏观物理体系，适用于所有连续力学系统，但作为具体描述方法还有一定局限，有待进一步发展。

Some Notes on the Variational Principles of Mechanics and Their Applications

This paper discusses the limitations of extension of classical Hamiltonian Principle to continuous systems, then reviews the new developments of operational theory in functional analysis and variational principles in non equilibrium thermodynamics based on field variation. Complementary dual variational principles including adjoined variational methods and generalized Green function method are bases of finite element analysis and boundary element analysis as well. From the point of view of physics, variational principles of macroscopic non equilibrium thermodynamic can be applied to all continuous mechanical systems. However, they have some limitations in application scope and remain to be developed.