El-Nabulsi模型下基于非标准Lagrange函数的动力学系统的Lie对称性与守恒量

Lie symmetries and conserved quantities for dynamical systems with non-standard Lagrangians based on El-Nabulsi models

研究El-Nabulsi模型下基于非标准Lagrange函数的动力学系统的Lie对称性与守恒量。提出了基于非标准Lagrange函数的变分问题,得到了系统的Euler-Lagrange方程;由广义加速度的不变性,给出了基于非标准Lagrange函数的满足Lie对称性的确定方程,建立了结构方程与守恒量;并举例说明。

We studied the Lie symmetries and conserved quantities of dynamical systems with non-standard La- grangians based on El-Nabulsi models. With the proposition of the variational problem with non-standard La- grangians, we obtained the Euler-Lagrange equations of the system. By the invariance of generalized acceleration, we gave the determining equations of Lie symmetries with non-standard Lagrangians, and established the structure equations and conserved quantities. Finally, two examples were given to illustrate the application of the results.