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The variational discretization of the constrained higher-order Lagrange-Poincaré equations

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dc.contributor.authorBloch, Anthony
dc.contributor.authorColombo, Leonardo
dc.contributor.authorJiménez Alburquerque, Fernando
dc.date.accessioned2026-01-19T18:26:48Z
dc.date.available2026-01-19T18:26:48Z
dc.date.issued2019-01-01
dc.descriptionThe registered version of this article, first published in Discrete and Continuous Dynamical Systems- Series A, is available online at the publisher's website: American Institute of Mathematical Sciences, https://doi.org/10.3934/dcds.2019013
dc.descriptionLa versión registrada de este artículo, publicado por primera vez en Discrete and Continuous Dynamical Systems- Series A, está disponible en línea en el sitio web del editor: American Institute of Mathematical Sciences, https://doi.org/10.3934/dcds.2019013
dc.description.abstractIn this paper we investigate a variational discretization for the class of mechanical systems in presence of symmetries described by the action of a Lie group which reduces the phase space to a (non-trivial) principal bundle. By introducing a discrete connection we are able to obtain the discrete constrained higher-order Lagrange-Poincaré equations. These equations describe the dynamics of a constrained Lagrangian system when the Lagrangian function and the constraints depend on higher-order derivatives such as the acceleration, jerk or jounces. The equations, under some mild regularity conditions, determine a well defined (local) flow which can be used to define a numerical scheme to integrate the constrained higher-order Lagrange-Poincaré equations. Optimal control problems for underactuated mechanical systems can be viewed as higher-order constrained variational problems. We study how a variational discretization can be used in the construction of variational integrators for optimal control of underactuated mechanical systems where control inputs act soley on the base manifold of a principal bundle (the shape space). Examples include the energy minimum control of an electron in a magnetic field and two coupled rigid bodies attached at a common center of mass.es
dc.description.provenanceMade available in DSpace on 2026-01-19T18:26:48Z (GMT). No. of bitstreams: 1 The variational discretization of the constrained higher-order.pdf: 593380 bytes, checksum: 6c10bbebe2b22f2060105eaef5e464ed (MD5) Previous issue date: 2019-01-01en
dc.description.versionversión final
dc.identifier.citationBloch, A., Colombo, L., & Jiménez, F. (2019). The variational discretization of the constrained higher-order lagrange-poincaré equations. Discrete and Continuous Dynamical Systems- Series A, 39(1), 309-344. https://doi.org/10.3934/DCDS.2019013
dc.identifier.doihttps://doi.org/10.3934/dcds.2019013
dc.identifier.eissn1553-5231
dc.identifier.issn1078-0947
dc.identifier.urihttps://hdl.handle.net/20.500.14468/31475
dc.journal.issue1
dc.journal.titleDiscrete and Continuous Dynamical Systems- Series A
dc.journal.volume39
dc.language.isoen
dc.page.final344
dc.page.initial309
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-nc-nd/4.0/deed.es
dc.subject12 Matemáticas
dc.subject.keywordsVariational integratorsen
dc.subject.keywordsdiscrete mechanical systemsen
dc.subject.keywordsdiscrete mechanical systemsen
dc.subject.keywordsLagrangePoincar´e equationsen
dc.subject.keywordsgeometric integrationen
dc.subject.keywordsdiscrete variational calculusen
dc.subject.keywordsordinary differential equationsen
dc.subject.keywordscontrol of mechanical systemsen
dc.subject.keywordsreduction by symmetriesen
dc.titleThe variational discretization of the constrained higher-order Lagrange-Poincaré equationsen
dc.typeartículoes
dc.typejournal articleen
dspace.entity.typePublication
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relation.isAuthorOfPublication.latestForDiscovery2e39e62c-a93f-46b7-aa64-7b2227e7a2dd
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