Discrete second order constrained Lagrangian systems: first results

Autores
Borda, Nicolás; Fernández, Javier; Grillo, Sergio Daniel
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We briefly review the notion of second order constrained (continuous) system (SOCS) and then propose a discrete time counterpart of it, which we naturally call discrete second order constrained system (DSOCS). To illustrate and test numerically our model, we construct certain integrators that simulate the evolution of two mechanical systems: a particle moving in the plane with prescribed signed curvature, and the inertia wheel pendulum with a Lyapunov constraint. In addition, we prove a local existence and uniqueness result for trajectories of DSOCSs. As a first comparison of the underlying geometric structures, we study the symplectic behavior of both SOCSs and DSOCSs.
Fil: Borda, Nicolás. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Fernández, Javier. Comisión Nacional de Energía Atómica. Gerencia del Area de Energía Nuclear. Instituto Balseiro; Argentina
Fil: Grillo, Sergio Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Universidad Nacional de Cuyo; Argentina
Materia
Geometric Mechanics
Discrete Mechanical Systems
Nonholonomic Mechanics
Second Order Constraints
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:11336/21939
Acceder
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Discrete second order constrained Lagrangian systems: first resultsBorda, NicolásFernández, JavierGrillo, Sergio DanielGeometric MechanicsDiscrete Mechanical SystemsNonholonomic MechanicsSecond Order Constraintshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1https://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1We briefly review the notion of second order constrained (continuous) system (SOCS) and then propose a discrete time counterpart of it, which we naturally call discrete second order constrained system (DSOCS). To illustrate and test numerically our model, we construct certain integrators that simulate the evolution of two mechanical systems: a particle moving in the plane with prescribed signed curvature, and the inertia wheel pendulum with a Lyapunov constraint. In addition, we prove a local existence and uniqueness result for trajectories of DSOCSs. As a first comparison of the underlying geometric structures, we study the symplectic behavior of both SOCSs and DSOCSs.Fil: Borda, Nicolás. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Fernández, Javier. Comisión Nacional de Energía Atómica. Gerencia del Area de Energía Nuclear. Instituto Balseiro; ArgentinaFil: Grillo, Sergio Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Universidad Nacional de Cuyo; ArgentinaAmerican Institute of Mathematical Sciences2013-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/21939Borda, Nicolás; Fernández, Javier; Grillo, Sergio Daniel; Discrete second order constrained Lagrangian systems: first results; American Institute of Mathematical Sciences; Journal of Geometric Mechanics; 5; 4; 12-2013; 381-3971941-4889CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://aimsciences.org/journals/displayArticlesnew.jsp?paperID=9519info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1312.1941info:eu-repo/semantics/altIdentifier/doi/10.3934/jgm.2013.5.381info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:08:38Zoai:ri.conicet.gov.ar:11336/21939instacron: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:34982025-09-03 10:08:38.512CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Discrete second order constrained Lagrangian systems: first results
title Discrete second order constrained Lagrangian systems: first results
spellingShingle Discrete second order constrained Lagrangian systems: first results
Borda, Nicolás
Geometric Mechanics
Discrete Mechanical Systems
Nonholonomic Mechanics
Second Order Constraints
title_short Discrete second order constrained Lagrangian systems: first results
title_full Discrete second order constrained Lagrangian systems: first results
title_fullStr Discrete second order constrained Lagrangian systems: first results
title_full_unstemmed Discrete second order constrained Lagrangian systems: first results
title_sort Discrete second order constrained Lagrangian systems: first results
dc.creator.none.fl_str_mv Borda, Nicolás
Fernández, Javier
Grillo, Sergio Daniel
author Borda, Nicolás
author_facet Borda, Nicolás
Fernández, Javier
Grillo, Sergio Daniel
author_role author
author2 Fernández, Javier
Grillo, Sergio Daniel
author2_role author
author
dc.subject.none.fl_str_mv Geometric Mechanics
Discrete Mechanical Systems
Nonholonomic Mechanics
Second Order Constraints
topic Geometric Mechanics
Discrete Mechanical Systems
Nonholonomic Mechanics
Second Order Constraints
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We briefly review the notion of second order constrained (continuous) system (SOCS) and then propose a discrete time counterpart of it, which we naturally call discrete second order constrained system (DSOCS). To illustrate and test numerically our model, we construct certain integrators that simulate the evolution of two mechanical systems: a particle moving in the plane with prescribed signed curvature, and the inertia wheel pendulum with a Lyapunov constraint. In addition, we prove a local existence and uniqueness result for trajectories of DSOCSs. As a first comparison of the underlying geometric structures, we study the symplectic behavior of both SOCSs and DSOCSs.
Fil: Borda, Nicolás. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Fernández, Javier. Comisión Nacional de Energía Atómica. Gerencia del Area de Energía Nuclear. Instituto Balseiro; Argentina
Fil: Grillo, Sergio Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Universidad Nacional de Cuyo; Argentina
description We briefly review the notion of second order constrained (continuous) system (SOCS) and then propose a discrete time counterpart of it, which we naturally call discrete second order constrained system (DSOCS). To illustrate and test numerically our model, we construct certain integrators that simulate the evolution of two mechanical systems: a particle moving in the plane with prescribed signed curvature, and the inertia wheel pendulum with a Lyapunov constraint. In addition, we prove a local existence and uniqueness result for trajectories of DSOCSs. As a first comparison of the underlying geometric structures, we study the symplectic behavior of both SOCSs and DSOCSs.
publishDate 2013
dc.date.none.fl_str_mv 2013-12
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/11336/21939
Borda, Nicolás; Fernández, Javier; Grillo, Sergio Daniel; Discrete second order constrained Lagrangian systems: first results; American Institute of Mathematical Sciences; Journal of Geometric Mechanics; 5; 4; 12-2013; 381-397
1941-4889
CONICET Digital
CONICET
url http://hdl.handle.net/11336/21939
identifier_str_mv Borda, Nicolás; Fernández, Javier; Grillo, Sergio Daniel; Discrete second order constrained Lagrangian systems: first results; American Institute of Mathematical Sciences; Journal of Geometric Mechanics; 5; 4; 12-2013; 381-397
1941-4889
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://aimsciences.org/journals/displayArticlesnew.jsp?paperID=9519
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1312.1941
info:eu-repo/semantics/altIdentifier/doi/10.3934/jgm.2013.5.381
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
dc.publisher.none.fl_str_mv American Institute of Mathematical Sciences
publisher.none.fl_str_mv American Institute of Mathematical Sciences
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 13.13397

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