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Dirac Structures in Vakonomic Mechanics

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dc.contributor.authorJiménez Alburquerque, Fernando
dc.contributor.authorYoshimura, Hiroaki
dc.date.accessioned2026-01-19T15:56:12Z
dc.date.available2026-01-19T15:56:12Z
dc.date.issued2014-11-11
dc.descriptionThe registered version of this article, first published in Journal of Geometry and Physics, is available online at the publisher's website: Elsevier, https://doi.org/10.1016/j.geomphys.2014.11.002
dc.descriptionLa versión registrada de este artículo, publicado por primera vez en Journal of Geometry and Physics, está disponible en línea en el sitio web del editor: Elsevier, https://doi.org/10.1016/j.geomphys.2014.11.002
dc.description.abstractIn this paper, we explore dynamics of the nonholonomic system called vakonomic mechanics in the context of Lagrange-Dirac dynamical systems using a Dirac structure and its associated Hamilton-Pontryagin variational principle. We first show the link between vakonomic mechanics and nonholonomic mechanics from the viewpoints of Dirac structures as well as Lagrangian submanifolds. Namely, we clarify that Lagrangian submanifold theory cannot represent nonholonomic mechanics properly, but vakonomic mechanics instead. Second, in order to represent vakonomic mechanics, we employ the space T Q×V∗, where a vakonomic Lagrangian is defined from a given Lagrangian (possibly degenerate) subject to nonholonomic constraints. Then, we show how implicit vakonomic Euler-Lagrange equations can be formulated by the Hamilton-Pontryagin variational principle for the vakonomic Lagrangian on the extended Pontryagin bundle (T Q ⊕ T∗Q) × V∗. Associated with this variational principle, we establish a Dirac structure on (T Q ⊕ T∗Q) × V∗ to define an intrinsic vakonomic Lagrange-Dirac system. Furthermore, we establish another construction for the vakonomic Lagrange-Dirac system using a Dirac structure on T∗Q × V∗, where we introduce a vakonomic Dirac differential. Lastly, we illustrate our theory of vakonomic Lagrange-Dirac systems by some examples such as the vakonomic skate and the vertical rolling coin.en
dc.description.provenanceMade available in DSpace on 2026-01-19T15:56:12Z (GMT). No. of bitstreams: 1 Dirac Structures in Vakonomic Mechanics.pdf: 831304 bytes, checksum: d3ab4794f82ed37ec4b4c5791561e093 (MD5) Previous issue date: 2014-11-11en
dc.description.versionversión final
dc.identifier.citationJiménez, F., & Yoshimura, H. (2015). Dirac structures in vakonomic mechanics. Journal of Geometry and Physics, 94, 158-178. https://doi.org/10.1016/J.GEOMPHYS.2014.11.002
dc.identifier.doihttps://doi.org/10.1016/j.geomphys.2014.11.002
dc.identifier.eissn1879-1662
dc.identifier.issn0393-0440
dc.identifier.urihttps://hdl.handle.net/20.500.14468/31464
dc.journal.titleJournal of Geometry and Physics
dc.journal.volume94
dc.language.isoen
dc.page.final178
dc.page.initial158
dc.publisherElsevier
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.keywordsDirac structuresen
dc.subject.keywordsVakonomic mechanicsen
dc.subject.keywordsNonholonomic mechanicsen
dc.subject.keywordsVariational principlesen
dc.subject.keywordsImplicit Lagrangian systemsen
dc.titleDirac Structures in Vakonomic Mechanicsen
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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