虚位移的 Четаев定义与微分变分原理的等价性  

The Четаев＇s Definition on Virtual Displacement and the Equivalence among Differential Variational Principles

作　　者：李天珍[1] 马林[1] 张宇[2] 陈占清[2] 

机构地区：[1]徐州工程学院,江苏徐州221008 [2]中国矿业大学,江苏徐州221008

出　　处：《徐州工程学院学报》2006年第9期75-78,共4页Journal of Xuzhou Istitute of Technology

摘　　要：虚位移的Четаев定义是分析力学发展史上具有深远影响的里程碑．它的诞生是分析力学发展到非线性非完整系统力学的标志，它的科学思想对于推动力学乃至整个自然科学的进步具有重要的作用．文章在简略评价虚位移的Четаев定义的科学思路和历史意义的基础上，讨论了约束的可能变元（可能位移、可能速度、可能加速度）及其微变空间性质，并认为应用虚位移的Четаев定义，可以在各种微变空间之间架起桥梁，进而得出D’Alembert-Lagrange原理、Jourdain～Bertrand原理和Gauss原理本质上是等价的．The Четаев＇s definition on virtual displacement is a milestone in the development of analytical mechanics, which marks that analytical mechanics had advanced to nonlinear nonholonomic stage, and the scientific thinking of which plays a very important role in the promotion of mechanics and even the whole of natural science. After a brief comment on the scientific thinking and historic meaning of Четаев＇s definition on virtual displacement, this paper proceeds to expound on constrained possible microvariational elements （possible displacement, possible velocity, and possible acceleration） and their microvariational spaces. It is held in this paper that the use of Четаев＇s definition on virtual displacement can bridge different microvariational spaces, arid D＇Alembert--Lagrange principle, Jourdain-Bertrand principle, and Gauss principle are equivalent in essence.

关 键 词：虚位移的Четаев定义 非线性非完整系统 微分变分原理 等价性 

分 类 号：O316[理学—一般力学与力学基础]