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Fractional damping through restricted calculus of variations

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dc.contributor.authorJiménez Alburquerque, Fernando
dc.contributor.authorOber-Blöbaum, Sina
dc.contributor.funderEngineering and Physical Sciences Research Council
dc.date.accessioned2026-01-19T16:25:48Z
dc.date.available2026-01-19T16:25:48Z
dc.date.issued2021-04-05
dc.descriptionThe registered version of this article, first published in Journal of Nonlinear Science,, is available online at the publisher's website: Springer, https://doi.org/10.1007/s00332-021-09700-w
dc.descriptionLa versión registrada de este artículo, publicado por primera vez en Journal of Nonlinear Science,, está disponible en línea en el sitio web del editor: Springer, https://doi.org/10.1007/s00332-021-09700-w
dc.description.abstractWe deliver a novel approach towards the variational description of Lagrangian mechanical systems subject to fractional damping by establishing a restricted Hamilton’s principle. Fractional damping is a particular instance of non-local (in time) damping, which is ubiquitous in mechanical engineering applications. The restricted Hamilton’s principle relies on including fractional derivatives to the state space, the doubling of curves (which implies an extra mirror system) and the restriction of the class of varied curves. We will obtain the correct dynamics and will show rigorously that the extra mirror dynamics is nothing but the principal one in reversed time; thus, the restricted Hamilton’s principle is not adding extra physics to the original system. The price to pay, on the other hand, is that the fractional damped dynamics is only a sufficient condition for the extremals of the action. In addition, we proceed to discretise the new principle. This discretisation provides a set of numerical integrators for the continuous dynamics that we denote Fractional Variational Integrators (FVIs). The discrete dynamics is obtained upon the same ingredients, say doubling of discrete curves and restriction of the discrete variations. We display the performance of the FVIs, which have local truncation order 1, in two examples. As other integrators with variational origin, for instance those generated by the discrete Lagrange–d’Alembert principle, they show a superior performance tracking the dissipative energy, in opposition to direct (order 1) discretisations of the dissipative equations, such as explicit and implicit Euler schemes.en
dc.description.provenanceMade available in DSpace on 2026-01-19T16:25:48Z (GMT). No. of bitstreams: 1 Fractional damping through restricted calculus of variations.pdf: 4396036 bytes, checksum: 487784f611b32c40016a53f359d3fb18 (MD5) Previous issue date: 2021-04-05en
dc.description.sponsorshipThis work has been funded by the EPSRC project: ‘’Fractional Variational Integration and Optimal Control”; ref: EP/P020402/1.
dc.description.versionversión final
dc.identifier.citationJiménez, F., & Ober-Blöbaum, S. (2021). Fractional Damping Through Restricted Calculus of Variations. Journal of Nonlinear Science, 31(2). https://doi.org/10.1007/S00332-021-09700-W
dc.identifier.doihttps://doi.org/10.1007/s00332-021-09700-w
dc.identifier.eissn1432-1467
dc.identifier.issn0938-8974
dc.identifier.urihttps://hdl.handle.net/20.500.14468/31467
dc.journal.issue2
dc.journal.titleJournal of Nonlinear Science,
dc.journal.volume31
dc.language.isoen
dc.publisherSpringer
dc.relation.centerE.T.S. de Ingenieros Industriales
dc.relation.departmentMatemática Aplicada I
dc.relation.projectidinfo:eu-repo/grantAgreement/EPSRC//EP-P020402-1
dc.rightsinfo:eu-repo/semantics/openAccess
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/deed.es
dc.subject12 Matemáticas
dc.subject.keywordsContinuous/discrete Lagrangian and Hamiltonian modelling · · · · ·en
dc.subject.keywordsFractional derivativesen
dc.subject.keywordsFractional dissipative systemsen
dc.subject.keywordsFractional differential equationsen
dc.subject.keywordsVariational principlesen
dc.subject.keywordsVariational integratorsen
dc.titleFractional damping through restricted calculus of variationsen
dc.typeartículoes
dc.typejournal articleen
dspace.entity.typePublication
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relation.isAuthorOfPublication.latestForDiscovery2e39e62c-a93f-46b7-aa64-7b2227e7a2dd
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