An extension of the dirac and gotay-nester theories of constraints for dirac dynamical systems

Autores
Cendra, Hernán; Etchechoury, María del Rosario; Ferraro, Sebastián J.
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.
Laboratorio de Electrónica Industrial, Control e Instrumentación
Materia
Ingeniería Mecánica
Constrained systems
Dirac structures
Implicit differential equations
Nonholonomic mechanics
Poisson geometry
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc-sa/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/85174
Acceder
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oai_identifier_str oai:sedici.unlp.edu.ar:10915/85174
network_acronym_str SEDICI
repository_id_str 1329
network_name_str SEDICI (UNLP)
spelling An extension of the dirac and gotay-nester theories of constraints for dirac dynamical systemsCendra, HernánEtchechoury, María del RosarioFerraro, Sebastián J.Ingeniería MecánicaConstrained systemsDirac structuresImplicit differential equationsNonholonomic mechanicsPoisson geometryThis 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.Laboratorio de Electrónica Industrial, Control e Instrumentación2014info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf167-236http://sedici.unlp.edu.ar/handle/10915/85174enginfo:eu-repo/semantics/altIdentifier/issn/1941-4889info:eu-repo/semantics/altIdentifier/doi/10.3934/jgm.2014.6.167info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/4.0/Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-29T11:16:24Zoai:sedici.unlp.edu.ar:10915/85174Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-29 11:16:25.246SEDICI (UNLP) - Universidad Nacional de La Platafalse
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, Hernán
Ingeniería Mecánica
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, Hernán
Etchechoury, María del Rosario
Ferraro, Sebastián J.
author Cendra, Hernán
author_facet Cendra, Hernán
Etchechoury, María del Rosario
Ferraro, Sebastián J.
author_role author
author2 Etchechoury, María del Rosario
Ferraro, Sebastián J.
author2_role author
author
dc.subject.none.fl_str_mv Ingeniería Mecánica
Constrained systems
Dirac structures
Implicit differential equations
Nonholonomic mechanics
Poisson geometry
topic Ingeniería Mecánica
Constrained systems
Dirac structures
Implicit differential equations
Nonholonomic mechanics
Poisson geometry
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.
Laboratorio de Electrónica Industrial, Control e Instrumentación
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
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Articulo
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://sedici.unlp.edu.ar/handle/10915/85174
url http://sedici.unlp.edu.ar/handle/10915/85174
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/issn/1941-4889
info:eu-repo/semantics/altIdentifier/doi/10.3934/jgm.2014.6.167
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
dc.format.none.fl_str_mv application/pdf
167-236
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
instname:Universidad Nacional de La Plata
instacron:UNLP
reponame_str SEDICI (UNLP)
collection SEDICI (UNLP)
instname_str Universidad Nacional de La Plata
instacron_str UNLP
institution UNLP
repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
repository.mail.fl_str_mv alira@sedici.unlp.edu.ar
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