一般完整系统Mei对称性的共形不变性与守恒量  

Conformal invariance and conserved quantities of Mei symmetry for general holonomic systems

作　　者：蔡建乐[1] 

机构地区：[1]杭州师范大学理学院,杭州310018

出　　处：《物理学报》2009年第1期22-27,共6页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:10572021;10772025);高等学校博士学科点专项科研基金(批准号:20040007022)资助的课题~~

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.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.

关 键 词：一般完整系统 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] O174.51[理学—力学]