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Variational integrators for underactuated mechanical control systems with symmetries

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dc.contributor.authorColombo, Leonardo
dc.contributor.authorJiménez Alburquerque, Fernando
dc.contributor.authorMartín de Diego, David
dc.date.accessioned2026-01-20T12:45:13Z
dc.date.available2026-01-20T12:45:13Z
dc.date.issued2016-05-01
dc.descriptionThe registered version of this article, first published in Journal of Computational Dynamics, is available online at the publisher's website: EDITOR, https://doi.org/10.3934/jcd.2015003
dc.descriptionLa versión registrada de este artículo, publicado por primera vez en Journal of Computational Dynamics, está disponible en línea en el sitio web del editor: EDITOR, https://doi.org/10.3934/jcd.2015003
dc.description.abstractOptimal control problems for underactuated mechanical systems can be seen as a higher-order variational problem subject to higher-order constraints (that is, when the Lagrangian function and the constraints depend on higher-order derivatives such as the acceleration, jerk or jounces). In this paper we discuss the variational formalism for the class of underactuated mechanical control systems when the configuration space is a trivial principal bundle and the construction of variational integrators for such mechanical control systems. An interesting family of geometric integrators can be defined using discretizations of the Hamilton's principle of critical action. This family of geometric integrators is called variational integrators, being one of their main properties the preservation of geometric features as the symplecticity, momentum preservation and good behavior of the energy. We construct variational integrators for higher-order mechanical systems on trivial principal bundles and their extension for higher-order constrained systems, paying particular attention to the case of underactuated mechanical systems.en
dc.description.provenanceMade available in DSpace on 2026-01-20T12:45:13Z (GMT). No. of bitstreams: 1 Variational integrators for underactuated mechanical control systems with symmetries.pdf: 605586 bytes, checksum: d08e4bb570e8a35004b10b4f36c43304 (MD5) Previous issue date: 2016-05-01en
dc.description.versionversión final
dc.identifier.citationColombo, L., Jiménez, F., & de Diego, D. M. (2015). Variational integrators for mechanical control systems with symmetries. Journal of Computational Dynamics, 2(2), 193-225. https://doi.org/10.3934/JCD.2015003
dc.identifier.doihttps://doi.org/10.3934/jcd.2015003
dc.identifier.eissn2158-2505
dc.identifier.issn2158-2491
dc.identifier.urihttps://hdl.handle.net/20.500.14468/31488
dc.journal.issue2
dc.journal.titleJournal of Computational Dynamics
dc.journal.volume2
dc.language.isoen
dc.page.final225
dc.page.initial193
dc.publisherAmerican Institute of Mathematical Sciences
dc.relation.centerE.T.S. de Ingenieros Industriales
dc.relation.departmentMatemática Aplicada I
dc.rightsinfo:eu-repo/semantics/openAccess
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/deed.es
dc.subject12 Matemáticas
dc.subject.keywordsVariational integratorsen
dc.subject.keywordshigher-order mechanicsen
dc.subject.keywordsunderactuated systemsen
dc.subject.keywordsoptimal controlen
dc.subject.keywordsdiscrete variational calculusen
dc.subject.keywordsconstrained mechanicsen
dc.titleVariational integrators for underactuated mechanical control systems with symmetriesen
dc.typeartículoes
dc.typejournal articleen
dspace.entity.typePublication
relation.isAuthorOfPublication2e39e62c-a93f-46b7-aa64-7b2227e7a2dd
relation.isAuthorOfPublication.latestForDiscovery2e39e62c-a93f-46b7-aa64-7b2227e7a2dd
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