THE RELATION BETWEEN THE MEI SYMMETRY AND THE NOETHER SYMMETRY-TAKING THE LAGRANGE SYSTEM AS AN EXAMPLE

This paper focuses on studying the relation between the Mei symmetry and the Noether symmetry, which takes the Lagrange system as an example. Based on the variational problem for Lagrangians under action of infinitesimal generator vectors, the Euler-Lagrange 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 Euler-Lagrange equations and 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 Lagrange system. In the end of the paper, we take the well-known Emden equation as example to illustrate the application of the results.