Variational and optimal control approaches for the second-order Herglotz problem on spheres

Bibliographic Details
Main Author: Machado, Luís
Publication Date: 2018
Other Authors: Abrunheiro, Lígia, Martins, Natália
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: http://hdl.handle.net/10773/24659
Summary: The present paper extends the classical second–order variational problem of Herglotz type to the more general context of the Euclidean sphere Sn following variational and optimal control approaches. The relation between the Hamiltonian equations and the generalized Euler-Lagrange equations is established. This problem covers some classical variational problems posed on the Riemannian manifold Sn such as the problem of finding cubic polynomials on S^n. It also finds applicability on the dynamics of the simple pendulum in a resistive medium.
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spelling Variational and optimal control approaches for the second-order Herglotz problem on spheresVariational problems of Herglotz typeHigher–order variational calculusHigher–order optimal control problemsRiemannian cubic polynomialsEuclidean sphereThe present paper extends the classical second–order variational problem of Herglotz type to the more general context of the Euclidean sphere Sn following variational and optimal control approaches. The relation between the Hamiltonian equations and the generalized Euler-Lagrange equations is established. This problem covers some classical variational problems posed on the Riemannian manifold Sn such as the problem of finding cubic polynomials on S^n. It also finds applicability on the dynamics of the simple pendulum in a resistive medium.Springer2018-11-16T15:25:37Z2019-01-01T00:00:00Z2019info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/24659eng0022-323910.1007/s10957-018-1424-0Machado, LuísAbrunheiro, LígiaMartins, 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:RCAAP2024-05-06T04:17:47Zoai:ria.ua.pt:10773/24659Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T14:03:45.253631Repositórios 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 Variational and optimal control approaches for the second-order Herglotz problem on spheres
title Variational and optimal control approaches for the second-order Herglotz problem on spheres
spellingShingle Variational and optimal control approaches for the second-order Herglotz problem on spheres
Machado, Luís
Variational problems of Herglotz type
Higher–order variational calculus
Higher–order optimal control problems
Riemannian cubic polynomials
Euclidean sphere
title_short Variational and optimal control approaches for the second-order Herglotz problem on spheres
title_full Variational and optimal control approaches for the second-order Herglotz problem on spheres
title_fullStr Variational and optimal control approaches for the second-order Herglotz problem on spheres
title_full_unstemmed Variational and optimal control approaches for the second-order Herglotz problem on spheres
title_sort Variational and optimal control approaches for the second-order Herglotz problem on spheres
author Machado, Luís
author_facet Machado, Luís
Abrunheiro, Lígia
Martins, Natália
author_role author
author2 Abrunheiro, Lígia
Martins, Natália
author2_role author
author
dc.contributor.author.fl_str_mv Machado, Luís
Abrunheiro, Lígia
Martins, Natália
dc.subject.por.fl_str_mv Variational problems of Herglotz type
Higher–order variational calculus
Higher–order optimal control problems
Riemannian cubic polynomials
Euclidean sphere
topic Variational problems of Herglotz type
Higher–order variational calculus
Higher–order optimal control problems
Riemannian cubic polynomials
Euclidean sphere
description The present paper extends the classical second–order variational problem of Herglotz type to the more general context of the Euclidean sphere Sn following variational and optimal control approaches. The relation between the Hamiltonian equations and the generalized Euler-Lagrange equations is established. This problem covers some classical variational problems posed on the Riemannian manifold Sn such as the problem of finding cubic polynomials on S^n. It also finds applicability on the dynamics of the simple pendulum in a resistive medium.
publishDate 2018
dc.date.none.fl_str_mv 2018-11-16T15:25:37Z
2019-01-01T00:00:00Z
2019
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/10773/24659
url http://hdl.handle.net/10773/24659
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0022-3239
10.1007/s10957-018-1424-0
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 Springer
publisher.none.fl_str_mv Springer
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
instacron:RCAAP
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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