准坐标下非完整奇异力学系统的Lie对称性与守恒量  

Lie Symmetries and Conserved Quantities of Nonholonomic Singular Mechanical Systems in Terms of Quasi-coordinates

作　　者：董丽鲜 梁景辉[1] 

机构地区：[1]山西师范大学物理与信息工程学院,山西临汾041004

出　　处：《江西科学》2015年第1期61-65,共5页Jiangxi Science

基　　金：山西省自然科学基金资助项目(20031008)

摘　　要：研究准坐标下非完整奇异力学系统的Lie对称性与守恒量。首先,定义准坐标下非完整奇异力学系统的无限小变换生成元,利用微分方程在无限小变换下的不变性,建立系统的确定方程。其次,给出结构方程并求出相应的守恒量。最后,研究Lie对称性逆问题举例说明结果的应用。This paper studies Lie symmetries and conserved quantities of nonholonomic singular mechanical systems in terms of quasi-coordinates. Firstly,we give the definition of the infinitesimal generator for the nonholonomic singular mechanical systems in terms of quasi-coordinates. Using the invariance of the differential equations under the infinitesimal transformations,we establish the determining equations of systems. Secondly,the structure equation and conserved quantities are given. Finally,we study the inverse problem of Lie symmetries. An example is given to illustrate the application of the result.

关 键 词：准坐标 非完整奇异力学系统 LIE对称性 守恒量 

分 类 号：O316[理学—一般力学与力学基础]