Un-reduction of systems of second-order ordinary differential equations

Autores
García-Toraño Andrés, Eduardo; Mestdag, Tom
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we consider an alternative approach to “un-reduction”. This is the process where one associates to a Lagrangian system on a manifold a dynamical system on a principal bundle over that manifold, in such a way that solutions project. We show that, when written in terms of second-order ordinary differential equations (SODEs), one may associate to the first system a (what we have called) “primary un-reduced SODE”, and we explain how all other un-reduced SODEs relate to it. We give examples that show that the considered procedure exceeds the realm of Lagrangian systems and that relate our results to those in the literature.
Fil: García-Toraño Andrés, Eduardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Matemática; Argentina
Fil: Mestdag, Tom. Universiteit Antwerp; Bélgica
Materia
LAGRANGIAN SYSTEM
PRINCIPAL CONNECTION
REDUCTION
SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS
SYMMETRY
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/60686

id CONICETDig_dac9a9afafc1ee265af620d8e70bc119
oai_identifier_str oai:ri.conicet.gov.ar:11336/60686
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Un-reduction of systems of second-order ordinary differential equationsGarcía-Toraño Andrés, EduardoMestdag, TomLAGRANGIAN SYSTEMPRINCIPAL CONNECTIONREDUCTIONSECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONSSYMMETRYhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we consider an alternative approach to “un-reduction”. This is the process where one associates to a Lagrangian system on a manifold a dynamical system on a principal bundle over that manifold, in such a way that solutions project. We show that, when written in terms of second-order ordinary differential equations (SODEs), one may associate to the first system a (what we have called) “primary un-reduced SODE”, and we explain how all other un-reduced SODEs relate to it. We give examples that show that the considered procedure exceeds the realm of Lagrangian systems and that relate our results to those in the literature.Fil: García-Toraño Andrés, Eduardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Matemática; ArgentinaFil: Mestdag, Tom. Universiteit Antwerp; BélgicaNational Academy of Sciences of Ukraine2016-12info: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/11336/60686García-Toraño Andrés, Eduardo; Mestdag, Tom; Un-reduction of systems of second-order ordinary differential equations; National Academy of Sciences of Ukraine; Symmetry, Integrability And Geometry; 12; 12-2016; 1-201815-0659CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.3842/SIGMA.2016.115info:eu-repo/semantics/altIdentifier/url/http://www.emis.de/journals/SIGMA/2016/115/info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1606.07649info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:54:05Zoai:ri.conicet.gov.ar:11336/60686instacron: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 09:54:05.35CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Un-reduction of systems of second-order ordinary differential equations
title Un-reduction of systems of second-order ordinary differential equations
spellingShingle Un-reduction of systems of second-order ordinary differential equations
García-Toraño Andrés, Eduardo
LAGRANGIAN SYSTEM
PRINCIPAL CONNECTION
REDUCTION
SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS
SYMMETRY
title_short Un-reduction of systems of second-order ordinary differential equations
title_full Un-reduction of systems of second-order ordinary differential equations
title_fullStr Un-reduction of systems of second-order ordinary differential equations
title_full_unstemmed Un-reduction of systems of second-order ordinary differential equations
title_sort Un-reduction of systems of second-order ordinary differential equations
dc.creator.none.fl_str_mv García-Toraño Andrés, Eduardo
Mestdag, Tom
author García-Toraño Andrés, Eduardo
author_facet García-Toraño Andrés, Eduardo
Mestdag, Tom
author_role author
author2 Mestdag, Tom
author2_role author
dc.subject.none.fl_str_mv LAGRANGIAN SYSTEM
PRINCIPAL CONNECTION
REDUCTION
SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS
SYMMETRY
topic LAGRANGIAN SYSTEM
PRINCIPAL CONNECTION
REDUCTION
SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS
SYMMETRY
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 consider an alternative approach to “un-reduction”. This is the process where one associates to a Lagrangian system on a manifold a dynamical system on a principal bundle over that manifold, in such a way that solutions project. We show that, when written in terms of second-order ordinary differential equations (SODEs), one may associate to the first system a (what we have called) “primary un-reduced SODE”, and we explain how all other un-reduced SODEs relate to it. We give examples that show that the considered procedure exceeds the realm of Lagrangian systems and that relate our results to those in the literature.
Fil: García-Toraño Andrés, Eduardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Matemática; Argentina
Fil: Mestdag, Tom. Universiteit Antwerp; Bélgica
description In this paper we consider an alternative approach to “un-reduction”. This is the process where one associates to a Lagrangian system on a manifold a dynamical system on a principal bundle over that manifold, in such a way that solutions project. We show that, when written in terms of second-order ordinary differential equations (SODEs), one may associate to the first system a (what we have called) “primary un-reduced SODE”, and we explain how all other un-reduced SODEs relate to it. We give examples that show that the considered procedure exceeds the realm of Lagrangian systems and that relate our results to those in the literature.
publishDate 2016
dc.date.none.fl_str_mv 2016-12
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/11336/60686
García-Toraño Andrés, Eduardo; Mestdag, Tom; Un-reduction of systems of second-order ordinary differential equations; National Academy of Sciences of Ukraine; Symmetry, Integrability And Geometry; 12; 12-2016; 1-20
1815-0659
CONICET Digital
CONICET
url http://hdl.handle.net/11336/60686
identifier_str_mv García-Toraño Andrés, Eduardo; Mestdag, Tom; Un-reduction of systems of second-order ordinary differential equations; National Academy of Sciences of Ukraine; Symmetry, Integrability And Geometry; 12; 12-2016; 1-20
1815-0659
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.3842/SIGMA.2016.115
info:eu-repo/semantics/altIdentifier/url/http://www.emis.de/journals/SIGMA/2016/115/
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1606.07649
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv National Academy of Sciences of Ukraine
publisher.none.fl_str_mv National Academy of Sciences of Ukraine
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_ 1842269263776186368
score 13.13397