非完整力学系统的Lie对称性直接导致的一种守恒量

doi:10.3969/j.issn.1000-1093.2012.11.011

兵工学报 ›› 2012, Vol. 33 ›› Issue (11): 1342-1345.doi: 10.3969/j.issn.1000-1093.2012.11.011

非完整力学系统的Lie对称性直接导致的一种守恒量

沈跃, 张令坦

（中国石油大学理学院，山东青岛 266580）

收稿日期:2011-05-09 修回日期:2011-05-09 上线日期:2014-01-10
作者简介:沈跃（1961—），男，副教授

A Kind of Conserved Quantity Induced by Lie Symmetry of Nonholonomic Mechanical System

SHEN Yue, ZHANG Ling-tan

（College of Science, China University of Petroleum, Qingdao 266580， Shandong, China）

Received:2011-05-09 Revised:2011-05-09 Online:2014-01-10

摘要/Abstract

摘要： 非完整约束力学系统对称性与守恒量的研究不仅具有重要的理论意义，而且具有重要的实际价值。利用无限小群变换分析方法研究了非完整力学系统的Lie对称性直接导致的一种守恒量，给出了系统Lie对称性的判据，得到了系统Lie对称性直接导致的一种守恒量存在的条件和形式，举例说明了结果的应用。

关键词: 一般力学, 非完整力学系统, Lie对称性, 守恒量

Abstract: It represents important not only theoretical but also practical significance to study the symmetry and conserved quantity of nonholonomic mechanical system. A kind of conserved quantity directly induced by Lie symmetry is studied by using infinitesimal group transformation analysis. Firstly, the criterion of Lie symmetry for nonholonomic mechanical system is given. Secondly, the existential condition of the conserved quantity and its forms are obtained. Finally, an example is given to illustrate the application of the results.

中图分类号:

O316

沈跃, 张令坦. 非完整力学系统的Lie对称性直接导致的一种守恒量[J]. 兵工学报, 2012, 33(11): 1342-1345.

SHEN Yue, ZHANG Ling-tan. A Kind of Conserved Quantity Induced by Lie Symmetry of Nonholonomic Mechanical System[J]. Acta Armamentarii, 2012, 33(11): 1342-1345.

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非完整力学系统的Lie对称性直接导致的一种守恒量

A Kind of Conserved Quantity Induced by Lie Symmetry of Nonholonomic Mechanical System

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