相空间中基于El-Nabulsi模型的Lie对称性与守恒量（英文）

Lie Symmetry and Conserved Quantity Based on El-Nabulsi Models in Phase Space

接要:研究相空间中基于El-Nabulsi非保守动力学模型的Lie对称性与守恒量.首先,建立系统的运动方程.其次,在一般无限小变换下,建立确定方程,从而给出相空间中基于El-Nabulsi模型的Lie对称性的定义和判据,同时,给出相空间中Lie对称性直接导致的广义Hojman守恒量,Hojman守恒量为广义Hojman守恒量一特例.然后,给出基于El-Nabulsi模型的Lie对称性导致的Noether守恒量.最后,给出2个特例说明结果的应用.

In phase space,the Lie symmetry and conserved quantity for non-conservative dynamics based on ElNabulsi models are studied. Firstly,the differential equations of motion of the systems are established. Secondly,the determining equations are established in phase space under a general infinitesimal transformation,thus the definition and the criterion of Lie symmetry based on El-Nabulsi models are obtained. At the same time,the form of generalized Hojman conserved quantity as a direct result of the Lie symmetry is given in phase space,and the Hojman conserved quantity acts as a special case of the generalized Hojman conserved quantity. Then,the Noether conserved quantity of the Lie symmetry based on El-Nabulsi models is gained. Lastly,two examples are given to illustrate the application of the results.