Table of Contents
Conference Papers in Mathematics
Volume 2013, Article ID 243621, 9 pages
Conference Paper

Geometric Hamiltonian Formulation of a Variational Problem Depending on the Covariant Acceleration

1Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
2ISCA, University of Aveiro, 3810-500 Aveiro, Portugal
3CMUC, Department of Mathematics, University of Coimbra, 3001-501 Coimbra, Portugal
4BIFI, Department of Theoretical Physics and Unidad Asociada IQFR-BIFI, University of Zaragoza, Edificio I+D, Campus Río Ebro, C/ Mariano Esquillor s/n, 50018 Zaragoza, Spain

Received 15 June 2013; Accepted 14 July 2013

Academic Editors: G. S. F. Frederico, N. Martins, and D. F. M. Torres

This Conference Paper is based on a presentation given by Lígia Abrunheiro at “The Cape Verde International Days on Mathematics 2013” held from 22 April 2013 to 25 April 2013 in Praia, Cape Verde.

Copyright © 2013 Lígia Abrunheiro et al. 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.


We consider a second-order variational problem depending on the covariant acceleration, which is related to the notion of Riemannian cubic polynomials. This problem and the corresponding optimal control problem are described in the context of higher order tangent bundles using geometric tools. The main tool, a presymplectic variant of Pontryagin’s maximum principle, allows us to study the dynamics of the control problem.