基于非标准Lagrange函数动力学系统的Mei对称性摄动与绝热不变量  

Perturbation of Mei Symmetries and Adiabatic Invariants for Dynamical Systems Based on Nonstandard Lagrangians

作　　者：王雪萍[1] 张毅[2] 

机构地区：[1]苏州科技大学数理学院,江苏苏州215009 [2]苏州科技大学土木工程学院,江苏苏州215011

出　　处：《吉林大学学报（理学版）》2017年第6期1569-1574,共6页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11572212;11272227);苏州科技大学研究生科研创新计划项目(批准号:SKCX15_062)

摘　　要：研究非标准Lagrange函数下动力学系统的Mei对称性摄动与绝热不变量.首先,给出系统的Euler-Lagrange方程与Mei对称性判据方程及精确不变量;其次,给出受小扰动后系统的运动微分方程,并研究该系统受小扰动作用下Mei对称性摄动与绝热不变量,得到了受扰动后系统的Mei型绝热不变量;最后,举例说明结果的应用.We studied the perturbation of Mei symmetries and adiabatic invariants for dynamical systems with nonstandard Lagrangians.Firstly,we gave the Euler-Lagrange equation of the system,the criterion equation to Mei symmetry and the exact invariants.Secondly,we gave the differential equations of motion of the system after a small disturbance,studied the perturbation of Mei symmetry and the adiabatic invariants for dynamical systems under a small disturbance,and obtained the Mei adiabatic invariants of the system after a small disturbance.Finally,we illustrated the application of the results.

关 键 词：非标准Lagrange函数 MEI对称性 摄动 绝热不变量 

分 类 号：O411[理学—理论物理]