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中文摘要：
研究一般完整系统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,定义一般完整系统动力学方程的Mei对称性共形不变性,借助Euler算子导出Mei对称性共形不变性的相关条件,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.
英文摘要：
Conformal invariance and conserved quantities of Mei symmetry for general holonomic systems are studied thoroughly.By introducing a single-parameter infinitesimal transformation group and its infinitesimal transformation vector of generators,definitions of the conformal invariance of Mei symmetry for the system 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,i.e.,Noether symmetry,Lie symmetry and Mei symmetry,are discussed.The system’s corresponding conserved quantities are obtained,according to the structure equation satisfied by the gauge function.Finally,an example is provided to illustrate how the given result can be applied.
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