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

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.