New developments on the geometric nonholonomic integrator

Autores
Ferraro, Sebastián José; Jiménez Alburquerque, Fernando; Martin de Diego, David
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper, we will discuss new developments regarding the geometric nonholonomic integrator (GNI) (Ferraro et al 2008 Nonlinearity 21 1911-28; Ferraro et al 2009 Discrete Contin. Dyn. Syst. (Suppl.) 220-9). GNI is a discretization scheme adapted to nonholonomic mechanical systems through a discrete geometric approach. This method was designed to account for some of the special geometric structures associated to a nonholonomic motion, like preservation of energy, preservation of constraints or the nonholonomic momentum equation. First, we study the GNI versions of the symplectic-Euler methods, paying special attention to their convergence behaviour. Then, we construct an extension of the GNI in the case of affine constraints. Finally, we generalize the proposed method to nonholonomic reduced systems, an important subclass of examples in nonholonomic dynamics. We illustrate the behaviour of the proposed method with the example of the inhomogeneous sphere rolling without slipping on a table.
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: Jiménez Alburquerque, Fernando. Universitat Technical Zu Munich; Alemania
Fil: Martin de Diego, David. Instituto de Ciencias Matemáticas; España
Materia
37j60
37m15
37n05
65p10
70-08
Affine Constraints Mathematics Subject Classification: 70f25
Discrete Variational Calculus
Geometric Nonholonomic Integrator
Nonholonomic Mechanics
Reduction by Symmetries
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:11336/77966
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/77966
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling New developments on the geometric nonholonomic integratorFerraro, Sebastián JoséJiménez Alburquerque, FernandoMartin de Diego, David37j6037m1537n0565p1070-08Affine Constraints Mathematics Subject Classification: 70f25Discrete Variational CalculusGeometric Nonholonomic IntegratorNonholonomic MechanicsReduction by Symmetrieshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper, we will discuss new developments regarding the geometric nonholonomic integrator (GNI) (Ferraro et al 2008 Nonlinearity 21 1911-28; Ferraro et al 2009 Discrete Contin. Dyn. Syst. (Suppl.) 220-9). GNI is a discretization scheme adapted to nonholonomic mechanical systems through a discrete geometric approach. This method was designed to account for some of the special geometric structures associated to a nonholonomic motion, like preservation of energy, preservation of constraints or the nonholonomic momentum equation. First, we study the GNI versions of the symplectic-Euler methods, paying special attention to their convergence behaviour. Then, we construct an extension of the GNI in the case of affine constraints. Finally, we generalize the proposed method to nonholonomic reduced systems, an important subclass of examples in nonholonomic dynamics. We illustrate the behaviour of the proposed method with the example of the inhomogeneous sphere rolling without slipping on a table.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; ArgentinaFil: Jiménez Alburquerque, Fernando. Universitat Technical Zu Munich; AlemaniaFil: Martin de Diego, David. Instituto de Ciencias Matemáticas; EspañaIOP Publishing2015-04-25info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/77966Ferraro, Sebastián José; Jiménez Alburquerque, Fernando; Martin de Diego, David; New developments on the geometric nonholonomic integrator; IOP Publishing; Nonlinearity; 28; 4; 25-4-2015; 871-9000951-7715CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://iopscience.iop.org/article/10.1088/0951-7715/28/4/871/metainfo:eu-repo/semantics/altIdentifier/doi/10.1088/0951-7715/28/4/871info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:08:27Zoai:ri.conicet.gov.ar:11336/77966instacron: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:34982025-09-10 13:08:27.483CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv New developments on the geometric nonholonomic integrator
title New developments on the geometric nonholonomic integrator
spellingShingle New developments on the geometric nonholonomic integrator
Ferraro, Sebastián José
37j60
37m15
37n05
65p10
70-08
Affine Constraints Mathematics Subject Classification: 70f25
Discrete Variational Calculus
Geometric Nonholonomic Integrator
Nonholonomic Mechanics
Reduction by Symmetries
title_short New developments on the geometric nonholonomic integrator
title_full New developments on the geometric nonholonomic integrator
title_fullStr New developments on the geometric nonholonomic integrator
title_full_unstemmed New developments on the geometric nonholonomic integrator
title_sort New developments on the geometric nonholonomic integrator
dc.creator.none.fl_str_mv Ferraro, Sebastián José
Jiménez Alburquerque, Fernando
Martin de Diego, David
author Ferraro, Sebastián José
author_facet Ferraro, Sebastián José
Jiménez Alburquerque, Fernando
Martin de Diego, David
author_role author
author2 Jiménez Alburquerque, Fernando
Martin de Diego, David
author2_role author
author
dc.subject.none.fl_str_mv 37j60
37m15
37n05
65p10
70-08
Affine Constraints Mathematics Subject Classification: 70f25
Discrete Variational Calculus
Geometric Nonholonomic Integrator
Nonholonomic Mechanics
Reduction by Symmetries
topic 37j60
37m15
37n05
65p10
70-08
Affine Constraints Mathematics Subject Classification: 70f25
Discrete Variational Calculus
Geometric Nonholonomic Integrator
Nonholonomic Mechanics
Reduction by Symmetries
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this paper, we will discuss new developments regarding the geometric nonholonomic integrator (GNI) (Ferraro et al 2008 Nonlinearity 21 1911-28; Ferraro et al 2009 Discrete Contin. Dyn. Syst. (Suppl.) 220-9). GNI is a discretization scheme adapted to nonholonomic mechanical systems through a discrete geometric approach. This method was designed to account for some of the special geometric structures associated to a nonholonomic motion, like preservation of energy, preservation of constraints or the nonholonomic momentum equation. First, we study the GNI versions of the symplectic-Euler methods, paying special attention to their convergence behaviour. Then, we construct an extension of the GNI in the case of affine constraints. Finally, we generalize the proposed method to nonholonomic reduced systems, an important subclass of examples in nonholonomic dynamics. We illustrate the behaviour of the proposed method with the example of the inhomogeneous sphere rolling without slipping on a table.
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: Jiménez Alburquerque, Fernando. Universitat Technical Zu Munich; Alemania
Fil: Martin de Diego, David. Instituto de Ciencias Matemáticas; España
description In this paper, we will discuss new developments regarding the geometric nonholonomic integrator (GNI) (Ferraro et al 2008 Nonlinearity 21 1911-28; Ferraro et al 2009 Discrete Contin. Dyn. Syst. (Suppl.) 220-9). GNI is a discretization scheme adapted to nonholonomic mechanical systems through a discrete geometric approach. This method was designed to account for some of the special geometric structures associated to a nonholonomic motion, like preservation of energy, preservation of constraints or the nonholonomic momentum equation. First, we study the GNI versions of the symplectic-Euler methods, paying special attention to their convergence behaviour. Then, we construct an extension of the GNI in the case of affine constraints. Finally, we generalize the proposed method to nonholonomic reduced systems, an important subclass of examples in nonholonomic dynamics. We illustrate the behaviour of the proposed method with the example of the inhomogeneous sphere rolling without slipping on a table.
publishDate 2015
dc.date.none.fl_str_mv 2015-04-25
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/11336/77966
Ferraro, Sebastián José; Jiménez Alburquerque, Fernando; Martin de Diego, David; New developments on the geometric nonholonomic integrator; IOP Publishing; Nonlinearity; 28; 4; 25-4-2015; 871-900
0951-7715
CONICET Digital
CONICET
url http://hdl.handle.net/11336/77966
identifier_str_mv Ferraro, Sebastián José; Jiménez Alburquerque, Fernando; Martin de Diego, David; New developments on the geometric nonholonomic integrator; IOP Publishing; Nonlinearity; 28; 4; 25-4-2015; 871-900
0951-7715
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/10.1088/0951-7715/28/4/871/meta
info:eu-repo/semantics/altIdentifier/doi/10.1088/0951-7715/28/4/871
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 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 12.993085

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