基于El-Nabulsi模型的分数阶Lagrange系统的Lie对称性与守恒量

Lie symmetry and conserved quantity of fractional Lagrange system based on El-Nabulsi models

研究基于El-Nabulsi模型的分数阶Lagrange系统的Lie对称性与守恒量。基于按Riemann-Liouville积分拓展的类分数阶变分问题导出El-Nabulsi模型的D'Alembert-Lagrange原理,得到系统的运动微分方程;给出分数阶Lie对称性的定义和判据,建立了Lie对称性确定方程,并提出广义Hojman定理,给出广义Hojman守恒量存在的条件及其形式;最后,建立了广义Noether定理,给出分数阶Lie对称性导致Noether守恒量的条件及其形式,并给出两个算例以说明结果的应用。

The Lie symmetry and the conserved quantity of fractional Lagrange system based on ElNabulsi models are studied. Firstly,the D＇Alembert-Lagrange principle of the El-Nabulsi models is deduced based on the fractional action-like variational problem which is expanded by the Riemann-Liouville integral,and the differential equations of motion of the system are obtained. Secondly,the definition and the criterion of the Lie symmetry are given,the determination equations of the Lie symmetry of the system are established,and the generalized Hojman theorem is put forward. At the same time,the existence condition and the form of the generalized Hojman conserved quantity are obtained. Then,the generalized Noether theorem is established,the existence condition and the form of the Noether conserved quantity led by the Lie symmetry are given. Finally,two examples are given to illustrate the application of the results.