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
.jpg)
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/60686
Ver los metadatos del registro completo
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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 Técnicas2025-09-29T09:54:21Zoai: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:34982025-09-29 09:54:22.018CONICET 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 |
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info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
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article |
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publishedVersion |
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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 |
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eng |
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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 |
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openAccess |
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National Academy of Sciences of Ukraine |
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National Academy of Sciences of Ukraine |
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