El-Nabulsi模型下非标准Lagrange函数的动力学系统的Noether定理  

Noether theorems for dynamical systems with non-standard Lagrangians based on El-Nabulsi models

作　　者：周小三[1] 张毅[2] 

机构地区：[1]苏州科技学院数理学院,苏州215009 [2]苏州科技学院土木工程学院,苏州215011

出　　处：《四川大学学报（自然科学版）》2017年第3期535-540,共6页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(10972151;11272227;11572212)

摘　　要：研究El-Nabulsi模型下基于非标准Lagrange函数的动力学系统的Noether定理.建立了基于指数Lagrange函数和Lagrange函数幂函数等两种非标准Lagrange函数的Hamilton原理,得到了系统的Euler-Lagrange方程;依据Hamilton作用量在无限小变换下的不变性,给出了Noether对称变换与准对称变换的条件,建立了动力学系统基于非标准Lagrange函数的Noether定理.文末举例说明结果的应用.The Noether theorems for dynamical systems with non-standard Lagrangians based on E1- Nabulsi models are studied. The Hamilton principles with exponential Lagrangians and power law Lagrangians are established respectively, and the Euler-Lagrange equations of the systems are obtained. The formulation of the conditions of Noether （quasi-） symmetrical transformations are given in terms of invariance of Hamilton action under infinitesimal transformation, the Noether theorems of dynamical systems with non-standard Lagrangians are established. At the end of the article, two examples are giv- en to illustrate the application of the results.

关 键 词：非标准Lagrange函数 HAMILTON原理 NOETHER定理 El-Nabulsi模型 

分 类 号：O316[理学—一般力学与力学基础]