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Title: The Herglotz variational problem on spheres and its optimal control approach
Author: Abrunheiro, Lígia
Machado, Luís
Martins, Natália
Keywords: Variational problems of Herglotz type
Calculus of variations
Optimal control problems
Geodesics on Riemannian manifolds
Euclidean sphere
Issue Date: 4-Jan-2016
Publisher: Ilirias Publications
Abstract: The main goal of this paper is to extend the generalized variational problem of Herglotz type to the more general context of the Euclidean sphere S^n. Motivated by classical results on Euclidean spaces, we derive the generalized Euler-Lagrange equation for the corresponding variational problem defined on the Riemannian manifold S^n. Moreover, the problem is formulated from an optimal control point of view and it is proved that the Euler-Lagrange equation can be obtained from the Hamiltonian equations. It is also highlighted the geodesic problem on spheres as a particular case of the generalized Herglotz problem.
Peer review: yes
ISSN: 2217-3412
Publisher Version:
Appears in Collections:CIDMA - Artigos
SCG - Artigos

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