An extension of the Dirac and Gotay-Nester theories of constraints for Dirac dynamical systems

Autores
Cendra, Hernan; Etchechoury, María del Rosario; Ferraro, Sebastián José
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
This paper extends the Gotay-Nester and the Dirac theories of constrained systems in order to deal with Dirac dynamical systems in the integrable case. Integrable Dirac dynamical systems are viewed as constrained systems where the constraint submanifolds are foliated. The cases considered usually in the literature correspond to a trivial foliation, with only one leaf. A Constraint Algorithm for Dirac dynamical systems (CAD), which extends the Gotay-Nester algorithm, is developed. Evolution equations are written using a Dirac bracket adapted to the foliations and an adapted total energy. The interesting example of LC circuits is developed in detail. The paper emphasizes the point of view that Dirac and Gotay-Nester theories are, in a certain sense, dual and that using a combination of results from both theories may have advantages in dealing with a given example, rather than using systematically one or the other.
Fil: Cendra, Hernan. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Matemática; Argentina
Fil: Etchechoury, María del Rosario. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
Fil: Ferraro, Sebastián José. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Matemática; Argentina
Materia
CONSTRAINED SYSTEMS
DIRAC STRUCTURES
IMPLICIT DIFFERENTIAL EQUATIONS
NONHOLONOMIC MECHANICS
POISSON GEOMETRY
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:11336/77932
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/77932
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling An extension of the Dirac and Gotay-Nester theories of constraints for Dirac dynamical systemsCendra, HernanEtchechoury, María del RosarioFerraro, Sebastián JoséCONSTRAINED SYSTEMSDIRAC STRUCTURESIMPLICIT DIFFERENTIAL EQUATIONSNONHOLONOMIC MECHANICSPOISSON GEOMETRYhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1This paper extends the Gotay-Nester and the Dirac theories of constrained systems in order to deal with Dirac dynamical systems in the integrable case. Integrable Dirac dynamical systems are viewed as constrained systems where the constraint submanifolds are foliated. The cases considered usually in the literature correspond to a trivial foliation, with only one leaf. A Constraint Algorithm for Dirac dynamical systems (CAD), which extends the Gotay-Nester algorithm, is developed. Evolution equations are written using a Dirac bracket adapted to the foliations and an adapted total energy. The interesting example of LC circuits is developed in detail. The paper emphasizes the point of view that Dirac and Gotay-Nester theories are, in a certain sense, dual and that using a combination of results from both theories may have advantages in dealing with a given example, rather than using systematically one or the other.Fil: Cendra, Hernan. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Matemática; ArgentinaFil: Etchechoury, María del Rosario. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; ArgentinaFil: Ferraro, Sebastián José. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Matemática; ArgentinaAmerican Institute of Mathematical Sciences2014-06info: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/11336/77932Cendra, Hernan; Etchechoury, María del Rosario; Ferraro, Sebastián José; An extension of the Dirac and Gotay-Nester theories of constraints for Dirac dynamical systems; American Institute of Mathematical Sciences; Journal of Geometric Mechanics; 6; 2; 6-2014; 167-2361941-48891941-4897CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=10062info:eu-repo/semantics/altIdentifier/doi/10.3934/jgm.2014.6.167info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1106.3354info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:26:28Zoai:ri.conicet.gov.ar:11336/77932instacron: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:34982025-09-29 10:26:29.019CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv An extension of the Dirac and Gotay-Nester theories of constraints for Dirac dynamical systems
title An extension of the Dirac and Gotay-Nester theories of constraints for Dirac dynamical systems
spellingShingle An extension of the Dirac and Gotay-Nester theories of constraints for Dirac dynamical systems
Cendra, Hernan
CONSTRAINED SYSTEMS
DIRAC STRUCTURES
IMPLICIT DIFFERENTIAL EQUATIONS
NONHOLONOMIC MECHANICS
POISSON GEOMETRY
title_short An extension of the Dirac and Gotay-Nester theories of constraints for Dirac dynamical systems
title_full An extension of the Dirac and Gotay-Nester theories of constraints for Dirac dynamical systems
title_fullStr An extension of the Dirac and Gotay-Nester theories of constraints for Dirac dynamical systems
title_full_unstemmed An extension of the Dirac and Gotay-Nester theories of constraints for Dirac dynamical systems
title_sort An extension of the Dirac and Gotay-Nester theories of constraints for Dirac dynamical systems
dc.creator.none.fl_str_mv Cendra, Hernan
Etchechoury, María del Rosario
Ferraro, Sebastián José
author Cendra, Hernan
author_facet Cendra, Hernan
Etchechoury, María del Rosario
Ferraro, Sebastián José
author_role author
author2 Etchechoury, María del Rosario
Ferraro, Sebastián José
author2_role author
author
dc.subject.none.fl_str_mv CONSTRAINED SYSTEMS
DIRAC STRUCTURES
IMPLICIT DIFFERENTIAL EQUATIONS
NONHOLONOMIC MECHANICS
POISSON GEOMETRY
topic CONSTRAINED SYSTEMS
DIRAC STRUCTURES
IMPLICIT DIFFERENTIAL EQUATIONS
NONHOLONOMIC MECHANICS
POISSON GEOMETRY
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv This paper extends the Gotay-Nester and the Dirac theories of constrained systems in order to deal with Dirac dynamical systems in the integrable case. Integrable Dirac dynamical systems are viewed as constrained systems where the constraint submanifolds are foliated. The cases considered usually in the literature correspond to a trivial foliation, with only one leaf. A Constraint Algorithm for Dirac dynamical systems (CAD), which extends the Gotay-Nester algorithm, is developed. Evolution equations are written using a Dirac bracket adapted to the foliations and an adapted total energy. The interesting example of LC circuits is developed in detail. The paper emphasizes the point of view that Dirac and Gotay-Nester theories are, in a certain sense, dual and that using a combination of results from both theories may have advantages in dealing with a given example, rather than using systematically one or the other.
Fil: Cendra, Hernan. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Matemática; Argentina
Fil: Etchechoury, María del Rosario. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
Fil: Ferraro, Sebastián José. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Matemática; Argentina
description This paper extends the Gotay-Nester and the Dirac theories of constrained systems in order to deal with Dirac dynamical systems in the integrable case. Integrable Dirac dynamical systems are viewed as constrained systems where the constraint submanifolds are foliated. The cases considered usually in the literature correspond to a trivial foliation, with only one leaf. A Constraint Algorithm for Dirac dynamical systems (CAD), which extends the Gotay-Nester algorithm, is developed. Evolution equations are written using a Dirac bracket adapted to the foliations and an adapted total energy. The interesting example of LC circuits is developed in detail. The paper emphasizes the point of view that Dirac and Gotay-Nester theories are, in a certain sense, dual and that using a combination of results from both theories may have advantages in dealing with a given example, rather than using systematically one or the other.
publishDate 2014
dc.date.none.fl_str_mv 2014-06
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/11336/77932
Cendra, Hernan; Etchechoury, María del Rosario; Ferraro, Sebastián José; An extension of the Dirac and Gotay-Nester theories of constraints for Dirac dynamical systems; American Institute of Mathematical Sciences; Journal of Geometric Mechanics; 6; 2; 6-2014; 167-236
1941-4889
1941-4897
CONICET Digital
CONICET
url http://hdl.handle.net/11336/77932
identifier_str_mv Cendra, Hernan; Etchechoury, María del Rosario; Ferraro, Sebastián José; An extension of the Dirac and Gotay-Nester theories of constraints for Dirac dynamical systems; American Institute of Mathematical Sciences; Journal of Geometric Mechanics; 6; 2; 6-2014; 167-236
1941-4889
1941-4897
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=10062
info:eu-repo/semantics/altIdentifier/doi/10.3934/jgm.2014.6.167
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1106.3354
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 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 13.070432

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