Четаев型非完整力学系统的微分几何原理

赵世鹰

Четаев型非完整力学系统的微分几何原理

赵世鹰

同济大学数学力学系

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出版历程
- 收稿日期: 1985-07-03
- 刊出日期: 1986-09-15

The Differentia, Geometric Principle of the Nonholonomic Mechanical Systems of Chetaev’s Type

Zhao Shi-ying

Tongji University, Shanghai

摘要

摘要: 本文应用现代微分几何的方法研究Четаев型非完整力学系统.通过恰当地定义Четаев型约束Pfaff系统,给出了非完整力学系统的微分几何结构,从而将带有非完整约束的Lagrange方程表达为一种与坐标无关的不变形式,并且采用这个新观点讨论了约束的嵌入和非完整力学系统的守恒定律等问题,得到了约束子流形上的Noether型定理.

Abstract: This paper deals with the nonholonomic mechanical systems of Chetaev's type by use of modern differential geometric methods.Based on a precise definition of Chetaev-type constraint pfaffian systems,the differential geometric structure is given for the description of nonholonomic mechanical systems.In thisframwork,the classical theory of Lagrange's equations with nonholonomic constraints is put into an invariant and coordinate free form.Furthermore,the problems of constraint imbedding and conservation laws are discussed within thisframwork,and the Noether-type thereom on constraint-imbedding submanifolds is obtained.

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参考文献(20)

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