基于非标准Lagrange函数的动力学系统的Lie对称性与Mei对称性  

On Lie symmetry and Mei symmetry for dynamical systems with non-standard Lagrangians

作　　者：周小三[1,2] 张毅 

机构地区：[1]苏州科技大学数理学院,江苏苏州215009 [2]句容中等专业学校,江苏镇江212499 [3]苏州科技大学土木工程学院,江苏苏州215011

出　　处：《云南大学学报（自然科学版）》2018年第1期66-73,共8页Journal of Yunnan University(Natural Sciences Edition)

基　　金：国家自然科学基金(11272227;11572212)

摘　　要：提出并研究在非标准Lagrange函数下动力学系统的Lie对称性与Mei对称性.基于系统的Lagrange方程,引入无限小变换及其生成元向量,给出了Lie对称性和Mei对称性的定义,建立了两类非标准Lagrange函数(指数Lagrange函数和幂律Lagrange函数)下动力学系统的Lie对称性结构方程和Mei对称性结构方程,导出了Lie对称性导致的Noether守恒量和Mei对称性导致的Mei守恒量,并结合算例说明结果的应用.The Lie symmetry and the Mei symmetry for dynamical systems with non-standard Lagrangians have been presented and studied. By introducing the infinitesimal transformations and their generating vectors, and in light of the Lagrange equations of the systems, the definitions of Lie symmetry and Mei symmetry have been given, and the structure equations of Lie symmetry and Mei symmetry for two types of dynamical systems with non -standard Lagrangians （ i. e. with exponential Lagrangians and power-law Lagrangians） have been established. The Noether conserved quantity resulted from Lie symmetry and the Mei conserved quantity resulted from Mei symme- try have been derived.In addition four examples have been given to illustrate the application of the results.

关 键 词：非标准Lagrange函数 LIE对称性 MEI对称性 守恒量 

分 类 号：O316[理学—一般力学与力学基础]