Table of Contents Author Guidelines Submit a Manuscript
Advances in Mathematical Physics
Volume 2014 (2014), Article ID 107895, 16 pages
http://dx.doi.org/10.1155/2014/107895
Research Article

On Conservation Forms and Invariant Solutions for Classical Mechanics Problems of Liénard Type

1Department of Mathematics, Faculty of Science and Letters, Istanbul Technical University, Maslak, 34469 Istanbul, Turkey
2Division of Mechanics, Faculty of Civil Engineering, Istanbul Technical University, Maslak, 34469 Istanbul, Turkey

Received 27 March 2014; Accepted 12 June 2014; Published 7 August 2014

Academic Editor: Jian-Qiang Sun

Copyright © 2014 Gülden Gün Polat and Teoman Özer. 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 study we apply partial Noether and -symmetry approaches to a second-order nonlinear autonomous equation of the form , called Liénard equation corresponding to some important problems in classical mechanics field with respect to and functions. As a first approach we utilize partial Lagrangians and partial Noether operators to obtain conserved forms of Liénard equation. Then, as a second approach, based on the -symmetry method, we analyze -symmetries for the case that -function is in the form of . Finally, a classification problem for the conservation forms and invariant solutions are considered.