准坐标下完整力学系统Lie对称性的共形不变性与守恒量

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

研究准坐标下完整力学系统Lie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Lie对称性的共形不变性,借助Euler算子导出Lie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。

Confovmal invariance and conserved quantities of Lie symmetry for holonomic mechanical systems in terms of quasi-coordinates. By introducing a single-parametet infinitesimal transformation group and its infinitesimal transformation vector of generators, definitions of conformal invariance of Lie 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 symmetry and Mei symmetry,are discussed. The system＇s corresponding conserved quantities are obtained, ac- cording to the structure equation satisfied by the gauge function. Finally, an example is provided to il- lustrate how the given result can be applied.