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Advances in Mathematical Physics
Volume 2017, Article ID 5164602, 13 pages
https://doi.org/10.1155/2017/5164602
Research Article

Symmetries and Properties of the Energy-Casimir Mapping in the Ball-Plate Problem

Department of Mathematics, Politehnica University of Timişoara, Piaţa Victoriei Nr. 2, 300006 Timişoara, Romania

Correspondence should be addressed to Tudor Bînzar; or.tpu@raznib.rodut

Received 3 August 2016; Revised 15 November 2016; Accepted 28 December 2016; Published 18 January 2017

Academic Editor: Juan C. Marrero

Copyright © 2017 Cristian Lăzureanu and Tudor Bînzar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this paper a system derived by an optimal control problem for the ball-plate dynamics is considered. Symplectic and Lagrangian realizations are given and some symmetries are studied. The image of the energy-Casimir mapping is described and some connections with the dynamics of the considered system are presented.