摘要
文章以Birkhoff系统为例研究Mei对称性与Noether对称性之间的关系.研究了基于无限小生成元向量作用下Birkhoff函数和Birkhoff函数组的变分问题,建立了该变分问题的Birkhoff方程与Noether对称性及其守恒量.研究表明:该变分问题得到的Birkhoff方程、Noether等式和Noether守恒量分别与经典Birkhoff系统Mei对称性的判据方程、结构方程和Mei守恒量完全一致.文末以著名的Emden方程等为例来说明结果的应用.
This paper focuses on studying the relation between the Mei symmetry and the Noether symmetry,takes the Birkhoff system as a example. The variational problem for Birkhoffian and Birkhoff＇s functions under action of infinitesimal generator vectors is studied. The Birkhoff＇ s equations for the variational problem are established. The Noether symmetry for the variational problem is studied and corresponding conserved quantity is given. The studies show that the Birkhoff equations the Noether identity and the Noether conserved quantity of the variational problem are exactly the same with the criterion equation and structural equation and the conserved quantity for Mei symmetry of classical Birkhoff system. In the end of the paper,we take the well-known Emden equation as example to illustrate the application of the results.
出处
《动力学与控制学报》
2016年第1期26-30,共5页
Journal of Dynamics and Control
基金
国家自然科学基金资助项目(10972151
11272227)~~
