非完整系统正则方程的Hamilton表述  

Hamiltonian Representation on Nonholonomic System

作　　者：马林[1] 

机构地区：[1]徐州工程学院土木工程学院,江苏徐州221008

出　　处：《湘潭大学自然科学学报》2009年第2期61-65,共5页Natural Science Journal of Xiangtan University

基　　金：国家自然科学基金资助项目(50674087)

摘　　要：基于虚位移的Четаев定义,利用两种方法导出了非完整系统的Hamilton正则方程.一种方法是从非完整系统的Lagrange描述中的Routh方程出发,通过Legendre变换而导出Hamilton正则方程;另一种方法是直接从Hamilton变分原理出发,即对非线性非完整约束求Hamilton变分,并引入Lagrange乘子,根据Lagrange乘子的任意性和广义坐标的Hamilton变分的独立性而导出Hamilton正则方程.对非完整系统的Hamilton表述进行了几点说明和解释.研究表明,只有采纳虚位移的Четаев定义,两种方法导出的Hamilton正则方程才完全相同.Based on Четаев＇s definition of virtual displacement, Hamilton＇s canonical Equations of nonholonomie system is built by two ways. The first way is through Legendre＇ s Transformation based on Routh＇s equation in the Lagrange＇s representation of nonholonomie system; the second way is based on Hamilton＇s variational principle： taking Hamilton＇s variation to the nonlinear, nonholonomic constraint equations, and using Lagrange＇s multiplier method to the nonholonomic system, during the derivation, the arbitrariness of Lagrange＇s multiplier and independence of Hamilton＇s variations are considered. Some ex- planations on Hamiltonian＇s representation of nonholonomie system are presented. It shows by this study that Hamilton＇s canonical Equations obtained by the two ways are the same because of the application of Четаев＇s definition of virtual displacement. Otherwise, the canonical Equations obtained by the second way are more complicate than that obtained by the first way.

关 键 词：虚位移的Четаев定义 微分变分原理 Hamilton变分原理 非完整系统 Hamilton描述 

分 类 号：O313[理学—一般力学与力学基础]