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Lie symmetries of the relative motion systems on time scales

  • Sheng-Nan Gong
  • Hui-Fang GaoEmail author
  • Jing-Li FuEmail author
Original Paper
  • 3 Downloads

Abstract

In this paper, the Lie symmetries and conserved quantities of the relative motion systems on time scales are proposed and studied. The Lagrange equations with delta derivatives on time scales are derived. By defining the infinitesimal transformations generators and using the invariance of differential equations under infinitesimal transformations, the determining equations of the Lie symmetries on time scales are established. Then, the structural equation and the form of conserved quantities of the Lie symmetries are given. Lie symmetries of the relative motion systems in discrete and continuous systems were discussed, respectively. Finally, an example is given to illustrate the applications of the conclusion.

Keywords

Time scale Lie symmetry The relative motion system 

PACS Nos.

02.20.Sv 11.30.-J 45.10.Db 45.20.Jj 

Notes

Acknowledgements

This work has been supported by the National Natural Science Foundation of China (Grant No. 11472247).

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Copyright information

© Indian Association for the Cultivation of Science 2019

Authors and Affiliations

  1. 1.Institute of Mathematical PhysicsZhejiang Sci-Tech UniversityHangzhouChina
  2. 2.The College of Electronics and InformationHangzhou Dianzi UniversityHangzhouChina
  3. 3.College of Mechanical and Automotive EngineeringZhejiang University of Water Resources and Electric PowerHangzhouChina

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