The Herglotz variational problem on spheres and its optimal control approach

Bibliographic Details
Main Author: Abrunheiro, Lígia
Publication Date: 2016
Other Authors: Machado, Luís, Martins, Natália
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: http://hdl.handle.net/10773/15635
Summary: 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.
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spelling The Herglotz variational problem on spheres and its optimal control approachVariational problems of Herglotz typeCalculus of variationsOptimal control problemsGeodesics on Riemannian manifoldsEuclidean sphereThe 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.Ilirias Publications2016-06-02T13:43:06Z2016-01-04T00:00:00Z2016-01-04info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/15635eng2217-3412Abrunheiro, LígiaMachado, LuísMartins, Natáliainfo:eu-repo/semantics/openAccessreponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2024-05-06T03:56:59Zoai:ria.ua.pt:10773/15635Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T13:52:13.705288Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
dc.title.none.fl_str_mv The Herglotz variational problem on spheres and its optimal control approach
title The Herglotz variational problem on spheres and its optimal control approach
spellingShingle The Herglotz variational problem on spheres and its optimal control approach
Abrunheiro, Lígia
Variational problems of Herglotz type
Calculus of variations
Optimal control problems
Geodesics on Riemannian manifolds
Euclidean sphere
title_short The Herglotz variational problem on spheres and its optimal control approach
title_full The Herglotz variational problem on spheres and its optimal control approach
title_fullStr The Herglotz variational problem on spheres and its optimal control approach
title_full_unstemmed The Herglotz variational problem on spheres and its optimal control approach
title_sort The Herglotz variational problem on spheres and its optimal control approach
author Abrunheiro, Lígia
author_facet Abrunheiro, Lígia
Machado, Luís
Martins, Natália
author_role author
author2 Machado, Luís
Martins, Natália
author2_role author
author
dc.contributor.author.fl_str_mv Abrunheiro, Lígia
Machado, Luís
Martins, Natália
dc.subject.por.fl_str_mv Variational problems of Herglotz type
Calculus of variations
Optimal control problems
Geodesics on Riemannian manifolds
Euclidean sphere
topic Variational problems of Herglotz type
Calculus of variations
Optimal control problems
Geodesics on Riemannian manifolds
Euclidean sphere
description 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.
publishDate 2016
dc.date.none.fl_str_mv 2016-06-02T13:43:06Z
2016-01-04T00:00:00Z
2016-01-04
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10773/15635
url http://hdl.handle.net/10773/15635
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 2217-3412
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Ilirias Publications
publisher.none.fl_str_mv Ilirias Publications
dc.source.none.fl_str_mv reponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
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instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron_str RCAAP
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reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
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