基于分数阶模型的Lagrange系统的积分因子与守恒量

Integrating factors and conserved quantities for Lagrange systems based on fractional order model

为了进一步研究基于分数阶模型的力学系统的守恒量,该文将积分因子方法应用于分数阶Lagrange系统,建立了寻找分数阶模型下Lagrange系统守恒量的一种新方法。首先,寻求分数阶Lagrange系统存在守恒量的必要条件和建立系统积分因子与守恒量的关系;其次,定义并给出用于确定积分因子的分数阶广义Killing方程;最后,得到基于分数阶模型的Lagrange系统的守恒量。文末举例说明结果的应用。

In order to further study the conserved quantities of mechanical systems based on fractional order model, we applied the method of integrating factors to the fractional order Lagrange system and proposed a new method for finding the conserved quantities of Lagrange systems based on fractional order model. First, we stud- ied the necessary conditions for the existence of the conserved quantities of the fractional order Lagrange systems and the relation between the conserved quantities and the integrating factors. Second, the fractional order gener-alized Killing equations used to determine the integrating factors were presented. Finally, we obtained the conserved quantities of the Lagrange systems based on fractional order model. Besides, an example was given to illustrate the application of the results.