Noether's theorem for higher-order variational problems of Herglotz type
Abstract
We approach higher-order variational problems of Herglotz type from an optimal control point of view. Using optimal control theory, we derive a generalized Euler-Lagrange equation, transversality conditions, a DuBois-Reymond necessary optimality condition and Noether's theorem for Herglotz's type higher-order variational problems, valid for piecewise smooth functions.
Cite
@article{arxiv.1507.05911,
title = {Noether's theorem for higher-order variational problems of Herglotz type},
author = {Simao P. S. Santos and Natalia Martins and Delfim F. M. Torres},
journal= {arXiv preprint arXiv:1507.05911},
year = {2015}
}
Comments
This is a preprint of a paper to appear in 'Discrete and Continuous Dynamical Systems', Supplement dedicated to the Proceedings of the 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications. Submitted 15-Sept-2014; accepted for publication, subject to a revision as suggested by the referees, 17-Jul-2015; revised 21-Jul-2015. arXiv admin note: text overlap with arXiv:1412.0433