基于非标准Lagrange函数的动力学系统的Noether-Mei对称性与守恒量

Noether-Mei symmetry and conserved quantity for dynamical systems with non-standard Lagrangians

研究基于两类非标准Lagrange函数(指数Lagrange函数和Lagrange幂函数)的动力学系统的NoetherMei对称性及其守恒量。首先,给出基于指数Lagrange函数和Lagrange幂函数的动力学系统的Noether-Mei对称性的定义与判据;其次,提出由系统的Noether-Mei对称性导致的Noether守恒量与Mei守恒量的存在条件及其形式,给出四个Noether-Mei对称性定理。最后,举例说明结果的应用。

This paper focuses on studying the Noether-Mei symmetry and the conserved quantity for dy- namical systems with non-standard Lagrangians （exponential Lagrangians and power law Lagrangians）. Firstly, The definition and the criteria of Noether-Mei symmetry for Lagrangians are given. Secondly, The conditions that Noether-Mei dynamical systems with non-standard symmetry leads to Noether conserved quantity or Mei conserved quantity and the form of conserved quantities are put forward. And four theo- rems for Noether-Mei symmetry and conserved quantities are established. Two examples are given to illus- trate the application of the results.