<abstract xmlns="http://www.w3.org/1999/xhtml"><p>This paper propose Noether symmetries and the conserved quantities of the relative motion systems on time scales. The Lagrange equations with delta derivatives on time scales are presented for the system. Based upon the invariance of Hamilton action on time scales, under the infinitesimal transformations with respect to the time and generalized coordinates, the Hamilton’s principle, the Noether theorems and conservation quantities are given for the systems on time scales. Lastly, an example is given to show the application the conclusion.</p></abstract>

This paper propose Noether symmetries and the conserved quantities of the relative motion systems on time scales. The Lagrange equations with delta derivatives on time scales are presented for the system. Based upon the invariance of Hamilton action on time scales, under the infinitesimal transformations with respect to the time and generalized coordinates, the Hamilton’s principle, the Noether theorems and conservation quantities are given for the systems on time scales. Lastly, an example is given to show the application the conclusion.

Noether’s theorems for the relative motion systems on time scales

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Noether\u2019s theorems for the relative motion systems on time scales"}

This paper propose Noether symmetries and the conserved quantities of the relative motion systems on time scales. The Lagrange equations with delta derivatives...

Noether’s theorems for the relative motion systems on time scales

Published Online: Dec 01, 2018

Page range: 513 - 526

Received: Aug 26, 2018

Accepted: Nov 26, 2018

DOI: https://doi.org/10.2478/AMNS.2018.2.00040

Keywords
time scale, Noether theorem, the relative motion systems

© 2018 Sheng-nan Gong and Jing-li Fu, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Noether’s theorems for the relative motion systems on time scales

Published Online: Dec 01, 2018

Page range: 513 - 526

Received: Aug 26, 2018

Accepted: Nov 26, 2018

DOI: https://doi.org/10.2478/AMNS.2018.2.00040

Keywordstime scale, Noether theorem, the relative motion systems

© 2018 Sheng-nan Gong and Jing-li Fu, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
time scale, Noether theorem, the relative motion systems