Kinematic reduction and the Hamilton-Jacobi equation

A close relationship between the classical Hamilton- Jacobi theory and the kinematic reduction of control systems by decoupling vector fields is shown in this paper. The geometric interpretation of this relationship relies on new mathematical techniques for mechanics defined on a skew-symmetric alge...

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Autores: Barbero Liñán, María, De León, Manuel, Martin de Diego, David, Marrero, Juan Carlos, Muñoz Lecanda, Miguel Carlos|||0000-0002-7037-0248
Tipo de recurso: artículo
Fecha de publicación:2012
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/19874
Acceso en línea:https://hdl.handle.net/2117/19874
https://dx.doi.org/10.3934/jgm.2012.4.207
Access Level:acceso abierto
Palabra clave:Hamilton-Jacobi equations
Decoupling vector fields
Hamilton-Jacobi equation
Kinematic reduction
Mechanical control systems
Skew-symmetric algebroids
Equacions de Hamilton-Jacobi
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències
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spelling Kinematic reduction and the Hamilton-Jacobi equationBarbero Liñán, MaríaDe León, ManuelMartin de Diego, DavidMarrero, Juan CarlosMuñoz Lecanda, Miguel Carlos|||0000-0002-7037-0248Hamilton-Jacobi equationsDecoupling vector fieldsHamilton-Jacobi equationKinematic reductionMechanical control systemsSkew-symmetric algebroidsEquacions de Hamilton-JacobiÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciènciesA close relationship between the classical Hamilton- Jacobi theory and the kinematic reduction of control systems by decoupling vector fields is shown in this paper. The geometric interpretation of this relationship relies on new mathematical techniques for mechanics defined on a skew-symmetric algebroid. This geometric structure allows us to describe in a simplified way the mechanics of nonholonomic systems with both control and external forces.Peer ReviewedAmerican Institute of Mathematical Sciences20122012-01-0120132013-07-09journal articlehttp://purl.org/coar/resource_type/c_6501AOhttp://purl.org/coar/version/c_b1a7d7d4d402bcceinfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/19874https://dx.doi.org/10.3934/jgm.2012.4.207reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)InglésengEuropean Commission http://dx.doi.org/10.13039/100011102 Seventh Framework Programme 246981 Geometric Mechanicsopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/198742026-05-27T15:37:01Z
dc.title.none.fl_str_mv Kinematic reduction and the Hamilton-Jacobi equation
title Kinematic reduction and the Hamilton-Jacobi equation
spellingShingle Kinematic reduction and the Hamilton-Jacobi equation
Barbero Liñán, María
Hamilton-Jacobi equations
Decoupling vector fields
Hamilton-Jacobi equation
Kinematic reduction
Mechanical control systems
Skew-symmetric algebroids
Equacions de Hamilton-Jacobi
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències
title_short Kinematic reduction and the Hamilton-Jacobi equation
title_full Kinematic reduction and the Hamilton-Jacobi equation
title_fullStr Kinematic reduction and the Hamilton-Jacobi equation
title_full_unstemmed Kinematic reduction and the Hamilton-Jacobi equation
title_sort Kinematic reduction and the Hamilton-Jacobi equation
dc.creator.none.fl_str_mv Barbero Liñán, María
De León, Manuel
Martin de Diego, David
Marrero, Juan Carlos
Muñoz Lecanda, Miguel Carlos|||0000-0002-7037-0248
author Barbero Liñán, María
author_facet Barbero Liñán, María
De León, Manuel
Martin de Diego, David
Marrero, Juan Carlos
Muñoz Lecanda, Miguel Carlos|||0000-0002-7037-0248
author_role author
author2 De León, Manuel
Martin de Diego, David
Marrero, Juan Carlos
Muñoz Lecanda, Miguel Carlos|||0000-0002-7037-0248
author2_role author
author
author
author
dc.subject.none.fl_str_mv Hamilton-Jacobi equations
Decoupling vector fields
Hamilton-Jacobi equation
Kinematic reduction
Mechanical control systems
Skew-symmetric algebroids
Equacions de Hamilton-Jacobi
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències
topic Hamilton-Jacobi equations
Decoupling vector fields
Hamilton-Jacobi equation
Kinematic reduction
Mechanical control systems
Skew-symmetric algebroids
Equacions de Hamilton-Jacobi
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències
description A close relationship between the classical Hamilton- Jacobi theory and the kinematic reduction of control systems by decoupling vector fields is shown in this paper. The geometric interpretation of this relationship relies on new mathematical techniques for mechanics defined on a skew-symmetric algebroid. This geometric structure allows us to describe in a simplified way the mechanics of nonholonomic systems with both control and external forces.
publishDate 2012
dc.date.none.fl_str_mv 2012
2012-01-01
2013
2013-07-09
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AO
http://purl.org/coar/version/c_b1a7d7d4d402bcce
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/19874
https://dx.doi.org/10.3934/jgm.2012.4.207
url https://hdl.handle.net/2117/19874
https://dx.doi.org/10.3934/jgm.2012.4.207
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv European Commission http://dx.doi.org/10.13039/100011102 Seventh Framework Programme 246981 Geometric Mechanics
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 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:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869404314044203008
score 15,300719

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