Mathews-Lakshmanan振子方程的分析力学解法  

ANALYTICAL MECHANICS METHODS FOR SOLVING MATHEWS-LAKSHMANAN OSCILLATOR

作　　者：李京颍[1] 丁光涛[2] 

机构地区：[1]阜阳师范学院物理与电子科学学院,阜阳236032 [2]安徽师范大学物理与电子信息学院,芜湖241000

出　　处：《动力学与控制学报》2018年第1期1-5,共5页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(11472063)~~

摘　　要：本文以求解非线性非保守的Mathews-Lakshmanan振子(以下简写成M-L振子)为例,说明分析力学理论和方法在非线性系统研究中的应用.根据变分法逆问题理论,将M-L振子方程变换为自伴随形式方程;利用四种方法构造出振子的拉格朗日函数和哈密顿函数;分别基于诺特理论和哈密顿-雅可比方法得到M-L振子方程的解.The solving of non-conservative and non-linear Mathews-Lakshmanan oscillator is taken as an example to illustrate the application of the theories and methods of analytical mechanics in studying the non-linear systems. According to the theories of inverse problem of variational calculus, the equation of M-L oscillator is transformed into a self-adjoint equation. The ods. Eventually, the equation of Lagrangian and Hamiltonian of M-L oscillator are also constructed by four meth- M-L oscillator is solved based on the Noether theory and the Hamilton-Jacobi method, respectively.

关 键 词：Mathews-Lakshmanan振子 变分法逆问题 非线性 分析力学 

分 类 号：O316[理学—一般力学与力学基础]