El-Nabulsi型非保守动力学系统的近似Noether不变量

Approximate Noether Invariants for Nonconservative Dynamical Systems Under El-Nabulsi Models

为了探究小扰动作用对动力学系统不变量的影响,研究El-Nabulsi指数模型和El-Nabulsi幂律模型下非保守系统的近似Noether不变量。根据Hamilton原理,并以非标准Lagrange函数作为其作用量泛函,建立非保守系统的El-Nabulsi型动力学方程。在此基础上,依据泛函在无限小变换下的不变性,给出非保守系统在小扰动作用下的近似Noether不变量。当未受扰动时,则给出精确Noether不变量。证明了El-Nabulsi指数模型和El-Nabulsi幂律模型下非保守系统的近似Noether不变量定理。本文方法为研究非保守系统动力学提供了一个新的思路,算例亦显示结果之有效性。

In order to investigate the influence of small perturbations on the invariants of dynamical systems, we study the approximate Noether invariants of nonconservative systems under El-Nabulsi exponential model and El-Nabulsi power-law model. According to Hamilton’s principle with nonstandard Lagrangians as its action functional, the dynamics equations of El-Nabulsi type for nonconservative systems are established. On this basis, due to the invariance of the functional under infinitesimal transformation, the approximate Noether invariants of nonconservative systems under small disturbance are obtained. When not disturbed, the exact Noether invariants are given. The approximate Noether invariant theorems for nonconservative systems under El-Nabulsi exponential model and El-Nabulsi power-law model are proved. This method provides a new idea for the study of nonconservative system dynamics, and two examples show the effectiveness of the results.