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

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.