Noether Theorem on Time Scales for Lagrangian Systems in Event Space

Time:2019-8-28

SHI Yufei1,2, ZHANG Yi3† 1. College of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou 215009, Jiangsu, China; 2. Wuxi Furen Middle School, Wuxi 214023, Jiangsu, China; 3. College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, Jiangsu, China

Abstract:

The Noether symmetry and the conserved quantity on time scales in event space are studied in this paper. Firstly, the Lagrangian of parameter forms on time scales in event space are established. The Euler-Lagrange equations and the second Euler-Lagrange equations of variational calculus on time scales in event space are established. Secondly, based upon the invariance of the Hamilton action on time scales in event space under the infinitesimal transformations of a group, the Noether symmetry and the conserved quantity on time scales in event space are established. Finally, an example is given to illustrate the method and results.

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