The inverse problem of the calculus of variations for discrete systems

Autores
Barbero Liñán, María; Farré Puiggalí, Marta; Ferraro, Sebastián José; Martin de Diego, David
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also provide a transition between the discrete and the continuous problems and propose variationality as an interesting geometric property to take into account in the design and computer simulation of numerical integrators for constrained systems. For instance, nonholonomic mechanics is generally non variational but some special cases admit an alternative variational description. We apply some standard nonholonomic integrators to such an example to study which ones conserve this property.
Fil: Barbero Liñán, María. Instituto de Ciencias Matemáticas; España. Universidad Politécnica de Madrid; España
Fil: Farré Puiggalí, Marta. Instituto de Ciencias Matemáticas; España
Fil: Ferraro, Sebastián José. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
Fil: Martin de Diego, David. Instituto de Ciencias Matemáticas; España
Materia
DISCRETE SECOND ORDER DIFFERENCE EQUATIONS
DISCRETE VARIATIONAL CALCULUS
INVERSE PROBLEM
NONHOLONOMIC MECHANICS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/91505
Acceder
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network_name_str CONICET Digital (CONICET)
spelling The inverse problem of the calculus of variations for discrete systemsBarbero Liñán, MaríaFarré Puiggalí, MartaFerraro, Sebastián JoséMartin de Diego, DavidDISCRETE SECOND ORDER DIFFERENCE EQUATIONSDISCRETE VARIATIONAL CALCULUSINVERSE PROBLEMNONHOLONOMIC MECHANICShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also provide a transition between the discrete and the continuous problems and propose variationality as an interesting geometric property to take into account in the design and computer simulation of numerical integrators for constrained systems. For instance, nonholonomic mechanics is generally non variational but some special cases admit an alternative variational description. We apply some standard nonholonomic integrators to such an example to study which ones conserve this property.Fil: Barbero Liñán, María. Instituto de Ciencias Matemáticas; España. Universidad Politécnica de Madrid; EspañaFil: Farré Puiggalí, Marta. Instituto de Ciencias Matemáticas; EspañaFil: Ferraro, Sebastián José. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaFil: Martin de Diego, David. Instituto de Ciencias Matemáticas; EspañaIOP Publishing2018-04-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/91505Barbero Liñán, María; Farré Puiggalí, Marta; Ferraro, Sebastián José; Martin de Diego, David; The inverse problem of the calculus of variations for discrete systems; IOP Publishing; Journal of Physics A: Mathematical and Theoretical; 51; 18; 9-4-2018; 1-39; 1852021751-8113CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://iopscience.iop.org/article/10.1088/1751-8121/aab546/metainfo:eu-repo/semantics/altIdentifier/doi/10.1088/1751-8121/aab546info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1708.04123info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T15:39:29Zoai:ri.conicet.gov.ar:11336/91505instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-15 15:39:29.439CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The inverse problem of the calculus of variations for discrete systems
title The inverse problem of the calculus of variations for discrete systems
spellingShingle The inverse problem of the calculus of variations for discrete systems
Barbero Liñán, María
DISCRETE SECOND ORDER DIFFERENCE EQUATIONS
DISCRETE VARIATIONAL CALCULUS
INVERSE PROBLEM
NONHOLONOMIC MECHANICS
title_short The inverse problem of the calculus of variations for discrete systems
title_full The inverse problem of the calculus of variations for discrete systems
title_fullStr The inverse problem of the calculus of variations for discrete systems
title_full_unstemmed The inverse problem of the calculus of variations for discrete systems
title_sort The inverse problem of the calculus of variations for discrete systems
dc.creator.none.fl_str_mv Barbero Liñán, María
Farré Puiggalí, Marta
Ferraro, Sebastián José
Martin de Diego, David
author Barbero Liñán, María
author_facet Barbero Liñán, María
Farré Puiggalí, Marta
Ferraro, Sebastián José
Martin de Diego, David
author_role author
author2 Farré Puiggalí, Marta
Ferraro, Sebastián José
Martin de Diego, David
author2_role author
author
author
dc.subject.none.fl_str_mv DISCRETE SECOND ORDER DIFFERENCE EQUATIONS
DISCRETE VARIATIONAL CALCULUS
INVERSE PROBLEM
NONHOLONOMIC MECHANICS
topic DISCRETE SECOND ORDER DIFFERENCE EQUATIONS
DISCRETE VARIATIONAL CALCULUS
INVERSE PROBLEM
NONHOLONOMIC MECHANICS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also provide a transition between the discrete and the continuous problems and propose variationality as an interesting geometric property to take into account in the design and computer simulation of numerical integrators for constrained systems. For instance, nonholonomic mechanics is generally non variational but some special cases admit an alternative variational description. We apply some standard nonholonomic integrators to such an example to study which ones conserve this property.
Fil: Barbero Liñán, María. Instituto de Ciencias Matemáticas; España. Universidad Politécnica de Madrid; España
Fil: Farré Puiggalí, Marta. Instituto de Ciencias Matemáticas; España
Fil: Ferraro, Sebastián José. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
Fil: Martin de Diego, David. Instituto de Ciencias Matemáticas; España
description We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also provide a transition between the discrete and the continuous problems and propose variationality as an interesting geometric property to take into account in the design and computer simulation of numerical integrators for constrained systems. For instance, nonholonomic mechanics is generally non variational but some special cases admit an alternative variational description. We apply some standard nonholonomic integrators to such an example to study which ones conserve this property.
publishDate 2018
dc.date.none.fl_str_mv 2018-04-09
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/91505
Barbero Liñán, María; Farré Puiggalí, Marta; Ferraro, Sebastián José; Martin de Diego, David; The inverse problem of the calculus of variations for discrete systems; IOP Publishing; Journal of Physics A: Mathematical and Theoretical; 51; 18; 9-4-2018; 1-39; 185202
1751-8113
CONICET Digital
CONICET
url http://hdl.handle.net/11336/91505
identifier_str_mv Barbero Liñán, María; Farré Puiggalí, Marta; Ferraro, Sebastián José; Martin de Diego, David; The inverse problem of the calculus of variations for discrete systems; IOP Publishing; Journal of Physics A: Mathematical and Theoretical; 51; 18; 9-4-2018; 1-39; 185202
1751-8113
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://iopscience.iop.org/article/10.1088/1751-8121/aab546/meta
info:eu-repo/semantics/altIdentifier/doi/10.1088/1751-8121/aab546
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1708.04123
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv IOP Publishing
publisher.none.fl_str_mv IOP Publishing
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.22299

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