准坐标下完整力学系统Mei对称性的共形不变性与守恒量  

Conformal Invariance and Conserved Quantities of Mei Symmetry for Holonomic Mechanical Systems in Terms of Quasi-coordinates

作　　者：党卫华[1] 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》2013年第4期433-438,共6页Jiangxi Science

基　　金：山西省自然科学基金资助项目(20031008)

摘　　要：研究准坐标下完整力学系统Mei对称性的共形不变性与守恒量。引入无限小单参数变换群及其生成元向量,定义准坐标下完整力学系统动力学方程的Mei对称性的共形不变性,借助Euler算子导出Mei对称性共形不变性的条件,给出其确定方程,讨论共形不变性与Noether对称性、Lie对称性以及Mei对称性之间的关系,利用规范函数满足的结构方程得到系统相应的守恒量,举例说明结果的应用。Conformal invariance and conserved quantities of Mei symmetry for holonomic mechanical systems in terms of quasi-coordinates . By introducing a single-parametet infinitesimal transformation group and its infinitesimal transformation vector of generator, definitions of conforrnal invariance of Mei symmetry for the systerm are provided. Conditions that the conformal invariance should satisfy are derived using the Euler operator, and their determining equations are then presented. Moreover, the relationship between conformal invariance and the three symmetries, Noether symmetry, Lie sym- metry and Mei symmetry, are discussed. The system＇s corresponding conserved quantities are ob- tained, according to the structure equation satisfied by the gauge function. Finally, an example is pro- vided to illustrate how the given result can be applied.

关 键 词：准坐标 完整力学系统 MEI对称性 共形不变性 守恒量 

分 类 号：O316[理学—一般力学与力学基础]