典型微扰力学系统的近似Lie对称性、近似Noether对称性和近似Mei对称性  

Approximate Lie Symmetries, Approximate Noether Symmetries and Approximate Mei Symmetries of Typical Perturbed Mechanical System

作　　者：楼智美[1] 王元斌[2] 谢志堃[1] 

机构地区：[1]绍兴文理学院物理系,绍兴312000 [2]绍兴文理学院数学系,绍兴312000

出　　处：《北京大学学报（自然科学版）》2016年第4期681-686,共6页Acta Scientiarum Naturalium Universitatis Pekinensis

基　　金：国家自然科学基金(11472177)资助

摘　　要：利用3种近似对称性方法(近似Lie对称性法、近似Noether对称性法和近似Mei对称性法)研究典型微扰力学系统的一阶近似对称性和近似守恒量。结果表明,利用近似Lie对称性法找到的6个一阶近似对称性和近似守恒量与利用近似Noether对称性法找到的相同,而利用近似Mei对称性法只能找到其中5个一阶近似对称性和近似守恒量。Three methods, which are approximate Lie symmetry method, approximate Noether symmetry method and approximate Mei symmetry method, are adopted to study the first order approximate symmetries and approximate conserved quantities of a typical perturbed mechanical system. Six identical first order approximate symmetries and approximate conserved quantities of the typical perturbed mechanical system are obtained by approximate Lie symmetry method and approximate Noether symmetry method, but only five of them can be obtained by approximate Mei symmetry method.

关 键 词：微扰力学系统 近似Lie对称性 近似Noether对称性 近似Mei对称性 近似守恒量 

分 类 号：O316[理学—一般力学与力学基础]