用高斯变分和Jourdain变分导出非完整约束系统的拉格朗日方程  

Using Gauss variation and Jourdain variation to derive Lagrange equations of nonholonomic constraint system

作　　者：张九铸 ZhANG Jiu-zhu(Longmen School of Jinchang City,Jinchang,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》2023年第10期20-23,共4页College Physics

摘　　要：文章认为,引入无法证明、几何意义不明确的Chetaev(Четаев)关系式研究非完整约束系统的运动是没必要的.实际上,只要将高斯变分代入动力学普遍方程,即可用拉格朗日待定乘子法导出一般性一阶非完整约束系统的含待定乘子的Lagrange方程,一阶线性非完整约束系统只是其特殊情形.如果一定要从约束方程导出后者,则可用Jourdain变分.这里的关键是分别正确写出系统的虚加速度、虚速度、虚位移所满足的方程.This paper argues that it is not necessary to use the unprovable and geometrically ambiguous Chetaev(Четаев)relations to study the motion of nonholonomic constraint systems.In fact,by applying the Gauss variation to the universal equations of dynamics,the Lagrange equation can be derived for a general first-order nonholonomic constraint system using the method of Lagrange multipliers,the first-order linear nonholonomic constraint system beings only its special case;if the latter must be derived from the constraint equation,the Jourdain variation can be used.The key here is to write the equations satisfied by the imaginary acceleration,imaginary velocity and imaginary displacement respectively correctly.

关 键 词：高斯变分 Jourdain 变分 非完整约束系统 Chetaev 条件 

分 类 号：O316[理学—一般力学与力学基础]