Reduction of Lagrangian mechanics on Lie algebroids

Detalhes bibliográficos
Autor(a) principal: Cariñena, José F.
Data de Publicação: 2007
Outros Autores: Costa, Joana M. Nunes da, Santos, Patrícia
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10316/4384
https://doi.org/10.1016/j.geomphys.2006.08.001
Resumo: We prove that if a surjective submersion which is a homomorphism of Lie algebroids is given, then there exists another homomorphism between the corresponding prolonged Lie algebroids and a relation between the dynamics on these Lie algebroid prolongations is established. We also propose a geometric reduction method for dynamics on Lie algebroids defined by a Lagrangian and the method is applied to regular Lagrangian systems with nonholonomic constraints.
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spelling Reduction of Lagrangian mechanics on Lie algebroidsReductionLie algebroidsLagrangian mechanicsWe prove that if a surjective submersion which is a homomorphism of Lie algebroids is given, then there exists another homomorphism between the corresponding prolonged Lie algebroids and a relation between the dynamics on these Lie algebroid prolongations is established. We also propose a geometric reduction method for dynamics on Lie algebroids defined by a Lagrangian and the method is applied to regular Lagrangian systems with nonholonomic constraints.http://www.sciencedirect.com/science/article/B6TJ8-4KSVG2C-1/1/4337b61b8426a38084b5017747203e712007info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleaplication/PDFhttp://hdl.handle.net/10316/4384http://hdl.handle.net/10316/4384https://doi.org/10.1016/j.geomphys.2006.08.001engJournal of Geometry and Physics. 57:3 (2007) 977-990Cariñena, José F.Costa, Joana M. Nunes daSantos, Patríciainfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2020-11-06T16:49:06Zoai:estudogeral.uc.pt:10316/4384Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:59:51.045229Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Reduction of Lagrangian mechanics on Lie algebroids
title Reduction of Lagrangian mechanics on Lie algebroids
spellingShingle Reduction of Lagrangian mechanics on Lie algebroids
Cariñena, José F.
Reduction
Lie algebroids
Lagrangian mechanics
title_short Reduction of Lagrangian mechanics on Lie algebroids
title_full Reduction of Lagrangian mechanics on Lie algebroids
title_fullStr Reduction of Lagrangian mechanics on Lie algebroids
title_full_unstemmed Reduction of Lagrangian mechanics on Lie algebroids
title_sort Reduction of Lagrangian mechanics on Lie algebroids
author Cariñena, José F.
author_facet Cariñena, José F.
Costa, Joana M. Nunes da
Santos, Patrícia
author_role author
author2 Costa, Joana M. Nunes da
Santos, Patrícia
author2_role author
author
dc.contributor.author.fl_str_mv Cariñena, José F.
Costa, Joana M. Nunes da
Santos, Patrícia
dc.subject.por.fl_str_mv Reduction
Lie algebroids
Lagrangian mechanics
topic Reduction
Lie algebroids
Lagrangian mechanics
description We prove that if a surjective submersion which is a homomorphism of Lie algebroids is given, then there exists another homomorphism between the corresponding prolonged Lie algebroids and a relation between the dynamics on these Lie algebroid prolongations is established. We also propose a geometric reduction method for dynamics on Lie algebroids defined by a Lagrangian and the method is applied to regular Lagrangian systems with nonholonomic constraints.
publishDate 2007
dc.date.none.fl_str_mv 2007
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/10316/4384
http://hdl.handle.net/10316/4384
https://doi.org/10.1016/j.geomphys.2006.08.001
url http://hdl.handle.net/10316/4384
https://doi.org/10.1016/j.geomphys.2006.08.001
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Journal of Geometry and Physics. 57:3 (2007) 977-990
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv aplication/PDF
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
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repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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