基于El-Nabulsi分数阶模型的广义经典力学系统Noether对称性摄动与绝热不变量（英文）

Noether symmetrical perturbation and adiabatic invariants for systems of generalized classical mechanics based on El-Nabulsi's fractional model

基于El-Nabuisi分数阶模型,研究了含高阶Euler-Lagrange方程的广义经典力学系统的精确不变量和绝热不变量。首先,基于广义El-Nabulsi-Hamilton作用量在无限小变换下的不变性,建立了未受扰动时广义经典力学系统的Noether理论,列出了Noether对称性和守恒量之间的内在关系。其次,引入高阶绝热不变量的概念,研究了El-Nabulsi模型下广义经典力学系统受小扰动作用后对称性的摄动问题,给出了Noether对称性的摄动导致的绝热不变量。最后,举例说明结果的应用。

Under the framework of El-Nabulsi's fractional model,we studied the exact invariants and adiabatic invariants for generalized classical mechanics system with high-order Euler-Lagrange equations.Firstly,based on the invariance of generalized El-Nabulsi-Hamilton action under the infinitesimal transformation,we established the Noether theorems for generalized classical mechanics system with no disturbance and explored the relationship between the Noether symmetries and the exact invariants.Secondly,we investigated the perturbation to Noether symmetries for the system under the action of small disturbance and obtained the adiabatic invariants caused by the perturbation to Noether symmetries.Finally,an example was given to illustrate the application of the results.