基于非标准Lagrange函数的动力学系统的Noether-Mei对称性与守恒量  

Noether-Mei symmetry and conserved quantity for dynamical systems with non-standard Lagrangians

作　　者：宋静[1] 张毅[2] 

机构地区：[1]苏州科技大学数理学院,江苏苏州215009 [2]苏州科技大学土木工程学院,江苏苏州215011

出　　处：《中山大学学报（自然科学版）》2017年第3期26-30,共5页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：国家自然科学基金(11272227;11572212);苏州科技大学研究生科研创新计划(SKYCX16_12)

摘　　要：研究基于两类非标准Lagrange函数(指数Lagrange函数和Lagrange幂函数)的动力学系统的NoetherMei对称性及其守恒量。首先,给出基于指数Lagrange函数和Lagrange幂函数的动力学系统的Noether-Mei对称性的定义与判据;其次,提出由系统的Noether-Mei对称性导致的Noether守恒量与Mei守恒量的存在条件及其形式,给出四个Noether-Mei对称性定理。最后,举例说明结果的应用。This paper focuses on studying the Noether-Mei symmetry and the conserved quantity for dy- namical systems with non-standard Lagrangians （exponential Lagrangians and power law Lagrangians）. Firstly, The definition and the criteria of Noether-Mei symmetry for Lagrangians are given. Secondly, The conditions that Noether-Mei dynamical systems with non-standard symmetry leads to Noether conserved quantity or Mei conserved quantity and the form of conserved quantities are put forward. And four theo- rems for Noether-Mei symmetry and conserved quantities are established. Two examples are given to illus- trate the application of the results.

关 键 词：非标准Lagrange函数 Noether-Mei对称性 NOETHER守恒量 MEI守恒量 

分 类 号：O316[理学—一般力学与力学基础]