Variational reduction of lagrangian systems with general constraints

Autores
Grillo, Sergio Daniel; Zuccalli, Marcela
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we present an alternative procedure for reducing, in the Lagrangian formalism, the equations of motion of first order constrained mechanical systems with symmetry. The procedure involves two principal connections: one of them is used to define the reduced degrees of freedom and the other one to decompose variations into horizontal and vertical components. On the one hand, we show that this new procedure is particularly useful when the configuration space is a trivial principal bundle over the symmetry group, which is the case of many interesting examples. On the other hand, based on that procedure, we extend in a natural way the variational reduction methods to the Lagrangian systems with higher order constraints. Examples are discussed in order to illustrate the involved theorethical constructions.
Fil: Grillo, Sergio Daniel. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina
Fil: Zuccalli, Marcela. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
Materia
Lagrangian systems
Variational reduction
Principal connections
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:11336/195172
Acceder
id CONICETDig_db4371fb4cecc91c6b14a322885460c7
oai_identifier_str oai:ri.conicet.gov.ar:11336/195172
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Variational reduction of lagrangian systems with general constraintsGrillo, Sergio DanielZuccalli, MarcelaLagrangian systemsVariational reductionPrincipal connectionshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we present an alternative procedure for reducing, in the Lagrangian formalism, the equations of motion of first order constrained mechanical systems with symmetry. The procedure involves two principal connections: one of them is used to define the reduced degrees of freedom and the other one to decompose variations into horizontal and vertical components. On the one hand, we show that this new procedure is particularly useful when the configuration space is a trivial principal bundle over the symmetry group, which is the case of many interesting examples. On the other hand, based on that procedure, we extend in a natural way the variational reduction methods to the Lagrangian systems with higher order constraints. Examples are discussed in order to illustrate the involved theorethical constructions.Fil: Grillo, Sergio Daniel. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; ArgentinaFil: Zuccalli, Marcela. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; ArgentinaAmerican Institute of Mathematical Sciences2012-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/195172Grillo, Sergio Daniel; Zuccalli, Marcela; Variational reduction of lagrangian systems with general constraints; American Institute of Mathematical Sciences; Journal of Geometric Mechanics; 4; 1; 4-2012; 49-881941-4889CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.aimsciences.org/article/doi/10.3934/jgm.2012.4.49info:eu-repo/semantics/altIdentifier/doi/10.3934/jgm.2012.4.49info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:33:45Zoai:ri.conicet.gov.ar:11336/195172instacron: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 10:33:45.503CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Variational reduction of lagrangian systems with general constraints
title Variational reduction of lagrangian systems with general constraints
spellingShingle Variational reduction of lagrangian systems with general constraints
Grillo, Sergio Daniel
Lagrangian systems
Variational reduction
Principal connections
title_short Variational reduction of lagrangian systems with general constraints
title_full Variational reduction of lagrangian systems with general constraints
title_fullStr Variational reduction of lagrangian systems with general constraints
title_full_unstemmed Variational reduction of lagrangian systems with general constraints
title_sort Variational reduction of lagrangian systems with general constraints
dc.creator.none.fl_str_mv Grillo, Sergio Daniel
Zuccalli, Marcela
author Grillo, Sergio Daniel
author_facet Grillo, Sergio Daniel
Zuccalli, Marcela
author_role author
author2 Zuccalli, Marcela
author2_role author
dc.subject.none.fl_str_mv Lagrangian systems
Variational reduction
Principal connections
topic Lagrangian systems
Variational reduction
Principal connections
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 present an alternative procedure for reducing, in the Lagrangian formalism, the equations of motion of first order constrained mechanical systems with symmetry. The procedure involves two principal connections: one of them is used to define the reduced degrees of freedom and the other one to decompose variations into horizontal and vertical components. On the one hand, we show that this new procedure is particularly useful when the configuration space is a trivial principal bundle over the symmetry group, which is the case of many interesting examples. On the other hand, based on that procedure, we extend in a natural way the variational reduction methods to the Lagrangian systems with higher order constraints. Examples are discussed in order to illustrate the involved theorethical constructions.
Fil: Grillo, Sergio Daniel. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina
Fil: Zuccalli, Marcela. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
description In this paper we present an alternative procedure for reducing, in the Lagrangian formalism, the equations of motion of first order constrained mechanical systems with symmetry. The procedure involves two principal connections: one of them is used to define the reduced degrees of freedom and the other one to decompose variations into horizontal and vertical components. On the one hand, we show that this new procedure is particularly useful when the configuration space is a trivial principal bundle over the symmetry group, which is the case of many interesting examples. On the other hand, based on that procedure, we extend in a natural way the variational reduction methods to the Lagrangian systems with higher order constraints. Examples are discussed in order to illustrate the involved theorethical constructions.
publishDate 2012
dc.date.none.fl_str_mv 2012-04
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/11336/195172
Grillo, Sergio Daniel; Zuccalli, Marcela; Variational reduction of lagrangian systems with general constraints; American Institute of Mathematical Sciences; Journal of Geometric Mechanics; 4; 1; 4-2012; 49-88
1941-4889
CONICET Digital
CONICET
url http://hdl.handle.net/11336/195172
identifier_str_mv Grillo, Sergio Daniel; Zuccalli, Marcela; Variational reduction of lagrangian systems with general constraints; American Institute of Mathematical Sciences; Journal of Geometric Mechanics; 4; 1; 4-2012; 49-88
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://www.aimsciences.org/article/doi/10.3934/jgm.2012.4.49
info:eu-repo/semantics/altIdentifier/doi/10.3934/jgm.2012.4.49
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
_version_ 1844614353251205120
score 13.070432

Publicaciones similares