Reduction by Symmetries of Contact Mechanical Systems on Lie Groups

We study the dynamics of contact mechanical systems on Lie groups that are invariant under a Lie group action. Analogously to standard mechanical systems on Lie groups, existing symmetries allow for reducing the number of equations. Thus, we obtain Euler-Poincar\'e-Herglotz equations on the ext...

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Autores: Anahory, A., Colombo, L.J., Leon, M.D., Marrero, J.C., Diego, D.M.D., Padrón, E.
Formato: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2024
País:España
Recursos:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/381563
Acesso em linha:http://hdl.handle.net/10261/381563
https://www.scopus.com/inward/record.uri?eid=2-s2.0-85201598106&doi=10.1137%2f23M1616935&partnerID=40&md5=94217f9e5294d175020b799815c097e0
Access Level:acceso abierto
Palavra-chave:Contact mechanical systems
Euler-Poincar\'e equations
Jacobi structures in mechanics
Lie–Poisson equations
Herglotz principle
Reduction by symmetries
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spelling Reduction by Symmetries of Contact Mechanical Systems on Lie GroupsAnahory, A.Colombo, L.J.Leon, M.D.Marrero, J.C.Diego, D.M.D.Padrón, E.Contact mechanical systemsEuler-Poincar\'e equationsJacobi structures in mechanicsLie–Poisson equationsHerglotz principleReduction by symmetriesWe study the dynamics of contact mechanical systems on Lie groups that are invariant under a Lie group action. Analogously to standard mechanical systems on Lie groups, existing symmetries allow for reducing the number of equations. Thus, we obtain Euler-Poincar\'e-Herglotz equations on the extended reduced phase space \frakg \times \BbbR associated with the extended phase space TG \times \BbbR, where the configuration manifold G is a Lie group and \frakg its Lie algebra. Furthermore, we obtain the Hamiltonian counterpart of these equations by studying the underlying Jacobi structure. Finally, we extend the reduction process to the case of symmetry-breaking systems which are invariant under a Lie subgroup of symmetries. © 2024 Society for Industrial and Applied Mathematics.The authors acknowledge financial support from Grant PID2019-106715GBC21 funded by MCIN/AEI/ 10.13039/501100011033. J.C. Marrero and E. Padr´on acknowledge financial support from the Spanish Ministry of Science and Innovation under grant PGC2018-098265-B-C32.Peer reviewedSociety for Industrial and Applied MathematicsMinisterio de Ciencia e Innovación (España)Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]202520252024info:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501Preprintinfo:eu-repo/semantics/submittedVersionapplication/pdfhttp://hdl.handle.net/10261/381563https://www.scopus.com/inward/record.uri?eid=2-s2.0-85201598106&doi=10.1137%2f23M1616935&partnerID=40&md5=94217f9e5294d175020b799815c097e0reponame:DIGITAL.CSIC. Repositorio Institucional del CSICinstname:Consejo Superior de Investigaciones Científicas (CSIC)Ingléshttps://doi.org/10.1137/23M1616935Síinfo:eu-repo/semantics/openAccessoai:digital.csic.es:10261/3815632026-05-22T06:33:51Z
dc.title.none.fl_str_mv Reduction by Symmetries of Contact Mechanical Systems on Lie Groups
title Reduction by Symmetries of Contact Mechanical Systems on Lie Groups
spellingShingle Reduction by Symmetries of Contact Mechanical Systems on Lie Groups
Anahory, A.
Contact mechanical systems
Euler-Poincar\'e equations
Jacobi structures in mechanics
Lie–Poisson equations
Herglotz principle
Reduction by symmetries
title_short Reduction by Symmetries of Contact Mechanical Systems on Lie Groups
title_full Reduction by Symmetries of Contact Mechanical Systems on Lie Groups
title_fullStr Reduction by Symmetries of Contact Mechanical Systems on Lie Groups
title_full_unstemmed Reduction by Symmetries of Contact Mechanical Systems on Lie Groups
title_sort Reduction by Symmetries of Contact Mechanical Systems on Lie Groups
dc.creator.none.fl_str_mv Anahory, A.
Colombo, L.J.
Leon, M.D.
Marrero, J.C.
Diego, D.M.D.
Padrón, E.
author Anahory, A.
author_facet Anahory, A.
Colombo, L.J.
Leon, M.D.
Marrero, J.C.
Diego, D.M.D.
Padrón, E.
author_role author
author2 Colombo, L.J.
Leon, M.D.
Marrero, J.C.
Diego, D.M.D.
Padrón, E.
author2_role author
author
author
author
author
dc.contributor.none.fl_str_mv Ministerio de Ciencia e Innovación (España)
Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]
dc.subject.none.fl_str_mv Contact mechanical systems
Euler-Poincar\'e equations
Jacobi structures in mechanics
Lie–Poisson equations
Herglotz principle
Reduction by symmetries
topic Contact mechanical systems
Euler-Poincar\'e equations
Jacobi structures in mechanics
Lie–Poisson equations
Herglotz principle
Reduction by symmetries
description We study the dynamics of contact mechanical systems on Lie groups that are invariant under a Lie group action. Analogously to standard mechanical systems on Lie groups, existing symmetries allow for reducing the number of equations. Thus, we obtain Euler-Poincar\'e-Herglotz equations on the extended reduced phase space \frakg \times \BbbR associated with the extended phase space TG \times \BbbR, where the configuration manifold G is a Lie group and \frakg its Lie algebra. Furthermore, we obtain the Hamiltonian counterpart of these equations by studying the underlying Jacobi structure. Finally, we extend the reduction process to the case of symmetry-breaking systems which are invariant under a Lie subgroup of symmetries. © 2024 Society for Industrial and Applied Mathematics.
publishDate 2024
dc.date.none.fl_str_mv 2024
2025
2025
dc.type.none.fl_str_mv info:eu-repo/semantics/article
http://purl.org/coar/resource_type/c_6501
Preprint
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10261/381563
https://www.scopus.com/inward/record.uri?eid=2-s2.0-85201598106&doi=10.1137%2f23M1616935&partnerID=40&md5=94217f9e5294d175020b799815c097e0
url http://hdl.handle.net/10261/381563
https://www.scopus.com/inward/record.uri?eid=2-s2.0-85201598106&doi=10.1137%2f23M1616935&partnerID=40&md5=94217f9e5294d175020b799815c097e0
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv https://doi.org/10.1137/23M1616935
Sí
dc.rights.none.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 Society for Industrial and Applied Mathematics
publisher.none.fl_str_mv Society for Industrial and Applied Mathematics
dc.source.none.fl_str_mv reponame:DIGITAL.CSIC. Repositorio Institucional del CSIC
instname:Consejo Superior de Investigaciones Científicas (CSIC)
instname_str Consejo Superior de Investigaciones Científicas (CSIC)
reponame_str DIGITAL.CSIC. Repositorio Institucional del CSIC
collection DIGITAL.CSIC. Repositorio Institucional del CSIC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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