Mei Symmetry of Time-Scales Euler-Lagrange Equations and Its Relation to Noether Symmetry
X.H. Zhaia, Y. Zhangb
aSchool of Science, Nanjing University of Science and Technology, Nanjing 210094, P.R. China
bCollege of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, P.R. China
Received: March 13, 2019; revised version April 23, 2019; in final form May 10, 2019
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In this paper, the Mei symmetry of the Euler-Lagrange equations on time-scales and its relation to the Noether symmetry are investigated. The definition and criterion of Mei symmetry of the Lagrangian system on time-scales are given. The conditions and forms of new conserved quantities which are found from the Mei symmetry of the system are derived. In addition, the Noether symmetry of a variational problem for Lagrangian on time-scales under the action of infinitesimal generator vectors and its corresponding conserved quantity are discussed. The results show that the Euler-Lagrange equations on time-scales, the Noether identity and the Noether conserved quantity of the variational problem under discussion are the same with the criterion equations, the structural equation, and the conserved quantity of the Mei symmetry for the original Lagrangian system on time-scales, respectively. In the end, two examples are provided to illustrate applications of the results.

DOI:10.12693/APhysPolA.136.439
PACS numbers: 11.10.Ef, 11.30.Na, 02.30.Hq