虚位移和理想约束系统的不同定义  

Different definitions of virtual displacement and ideally constrained system

作　　者：张九铸 ZHANG Jiu-zhu(Longmen School of Jinchuan Education Group of Jinchang City,Gansu 737104,China)

机构地区：[1]金昌市龙门学校,甘肃金昌737104

出　　处：《大学物理》2024年第9期12-14,34,共4页College Physics

摘　　要：关于理想的、一般性一阶非完整约束系统,这篇文章认为,虚位移满足的关系式即Chetaev关系式是可以被导出的,但该式中的虚位移应当指的是高斯变分.同样,要从动力学普遍方程出发,借助Chetaev关系式导出系统的带乘子的拉格朗日方程,首先需要判断系统是否为理想约束系统,但理想约束条件式中的虚位移也应当指的是高斯变分.对于理想的、一阶线性非完整约束系统,虚位移所满足的关系式和理想约束条件式中,采用的虚位移既可以是高斯变分,也可以是Jourdain变分.For ideal,general first-order nonholonomic constrained systems,this paper argues that the relation satisfied by the virtual displacement,namely Chetaev relation,can be derived,but the virtual displacement in the relation should refer tOthe Gauss variation.Similarly,in order tOderive the Lagrange equation with multipliers from the general equations of dynamics using Chetaev relations,it is necessary tOfirst determine whether the system is an ideal constrained system,and the virtual displacement in the ideal constraint conditions should alsOrefer tOthe Gauss variation.For an ideal,first-order linear nonholonomic constrained system,in the relation and ideal constraint conditions satisfied by the virtual displacement,the virtual displacement can be either Gauss variation or Jourdain variation.

关 键 词：非完整约束系统 Chetaev关系式 虚位移 高斯变分 Jourdain变分 理想约束系统 

分 类 号：O316[理学—一般力学与力学基础]