基于分数阶模型的非保守Hamilton系统Lie对称性研究

Lie symmetry of non-conservative Hamilton system based on fractional model

为了进一步揭示动力学系统的对称性和守恒量之间的内在联系,基于分数阶模型提出并研究非保守Hamilton系统的Lie对称性与守恒量.首先,依据非保守系统的Hamilton原理导出了基于分数阶模型的Hamilton正则方程.其次,在群的无限小变换下,给出了Lie对称性的确定方程,建立了分数阶模型下非保守Hamilton系统的Lie对称性的定义,并给出Lie对称性导致一类新型分数阶Noether守恒量的条件及其形式.最后,给出一个算例说明结果的应用.

To further reveal the inner relationship between the symmetry and the conserved quantity for a dynamical system, the Lie symmetry and the conserved quantity for a non-conservative Hamilton system based on fractional model are proposed and studied. Firstly, the fractional Hamilton canonical equations are established based on the fractional Hamilton principle for the non-conservative system. Secondly, the determining equations under the infinitesimal transformations of a group are given, and the definition of the Lie symmetry for the non-conservative Hamilton system under fractional model is established. The condition under which a Lie symmetry can lead to a new type of fractional Noether conserved quanti- ty is gained and the form of the conserved quantity is presented. Finally, an example is given to illus- trate the application of the results.