具有单面非完整约束的力学系统的Lie对称性与守恒量

数学物理学报 ›› 2000, Vol. 20 ›› Issue (1): 95-100.

具有单面非完整约束的力学系统的Lie对称性与守恒量

苏州城建环保学院基础部苏州 215011 北京理工大学应用力学系北京 100081

出版日期:2000-01-07 发布日期:2000-01-07

Lie Symmetries and Conserved Quantities of Nonholonomic Mechanical Systems with Unilateral Constraints

Department of Basic Courses, Suzhou Institute of Urban Construction &|Environmental Protection, Suzhou 215011 Department of Applied Mechanics, Beijing Institute of Technology, Beijing 100081

Online:2000-01-07 Published:2000-01-07

摘要/Abstract

摘要：

研究具有单面非完整约束的力学系统的Lie对称性. 给出由Lie对称性得到系统守恒量的条件和守恒量的形式，并研究上述问题的逆问题，即根据系统的已知积分来求相应的Lie对称性，最后举例说明结果的应用

关键词: 分析力学, 单面约束, 非完整约束, Lie对称性, 守恒量, 逆问题.

Abstract:

This paper studies the Lie symmetries of nonholonomic mechanical systems with unilateral constraints. It gives the conditions and the form of conserved quantities due to the Lie symmetries of the systems, and presents the inverse problem of the above problem, i.e., finding the corresponding Lie symmetry transformation according to a given integral of the systems. Finally, it gives an example to illustrate the application of the results.

Key words: Analytical mechanics ')"> Analytical mechanics , Unilateral constraint, Nonholonomic constraint, Lie symmetry, Conserved quantity, inverse problem

中图分类号:

张毅 |梅凤翔. 具有单面非完整约束的力学系统的Lie对称性与守恒量[J]. 数学物理学报, 2000, 20(1): 95-100.

Zhang Yi | Mei Fengxiang. Lie Symmetries and Conserved Quantities of Nonholonomic Mechanical Systems with Unilateral Constraints[J]. Acta mathematica scientia,Series A, 2000, 20(1): 95-100.

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