A general framework for nonholonomic mechanics: Nonholonomic Systems on Lie affgebroids

50 pages.-- Pre-print archive.-- PACS: 45.05.+x; 02.20.Sv; 02.40.Hw

Bibliographic Details
Authors: Iglesias, David, Marrero, Juan Carlos, Martin de Diego, David, Sosa, Diana
Format: article
Publication Date:2007
Country:España
Institution:Consejo Superior de Investigaciones Científicas (CSIC)
Repository:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/2281
Online Access:http://hdl.handle.net/10261/2281
Access Level:Open access
Keyword:Lie algebroids
Lie affgebroids
Lagrangian Mechanics
Hamiltonian Mechanics
Nonholonomic mechanics
Lagrange-d’Alembert equations
Projectors
AV-bundles
Aff-Poisson brackets
Non-holonomic brackets
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oai_identifier_str oai:digital.csic.es:10261/2281
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spelling A general framework for nonholonomic mechanics: Nonholonomic Systems on Lie affgebroidsIglesias, DavidMarrero, Juan CarlosMartin de Diego, DavidSosa, DianaLie algebroidsLie affgebroidsLagrangian MechanicsHamiltonian MechanicsNonholonomic mechanicsLagrange-d’Alembert equationsProjectorsAV-bundlesAff-Poisson bracketsNon-holonomic brackets50 pages.-- Pre-print archive.-- PACS: 45.05.+x; 02.20.Sv; 02.40.HwThis paper presents a geometric description of Lagrangian and Hamiltonian systems on Lie affgebroids subject to affine nonholonomic constraints. We define the notion of nonholonomically constrained system, and characterize regularity conditions that guarantee that the dynamics of the system can be obtained as a suitable projection of the unconstrained dynamics. It is shown that one can define an almost aff-Poisson bracket on the constraint AV-bundle, which plays a prominent role in the description of nonholonomic dynamics. Moreover, these developments give a general description of nonholonomic systems and the unified treatment permits to study nonholonomic systems after or before reduction in the same framework. Also, it is not necessary to distinguish between linear or affine constraints and the methods are valid for explicitly time-dependent systems.This work has been partially supported by MEC (Spain) Grants MTM 2006-03322, MTM 2004-7832, project “Ingenio Mathematica” (i-MATH) No. CSD 2006-00032 (Consolider-Ingenio 2010) and S-0505/ESP/0158 of the CAM. D. Iglesias wants to thank MEC for a Research Contract “Juan de la Cierva”.Peer reviewedAmerican Institute of Physics200720072007info:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501http://hdl.handle.net/10261/2281reponame:DIGITAL.CSIC. Repositorio Institucional del CSICinstname:Consejo Superior de Investigaciones Científicas (CSIC)Ingléshttp://dx.doi.org/10.1063/1.2776845info:eu-repo/semantics/openAccessoai:digital.csic.es:10261/22812026-05-22T06:33:51Z
dc.title.none.fl_str_mv A general framework for nonholonomic mechanics: Nonholonomic Systems on Lie affgebroids
title A general framework for nonholonomic mechanics: Nonholonomic Systems on Lie affgebroids
spellingShingle A general framework for nonholonomic mechanics: Nonholonomic Systems on Lie affgebroids
Iglesias, David
Lie algebroids
Lie affgebroids
Lagrangian Mechanics
Hamiltonian Mechanics
Nonholonomic mechanics
Lagrange-d’Alembert equations
Projectors
AV-bundles
Aff-Poisson brackets
Non-holonomic brackets
title_short A general framework for nonholonomic mechanics: Nonholonomic Systems on Lie affgebroids
title_full A general framework for nonholonomic mechanics: Nonholonomic Systems on Lie affgebroids
title_fullStr A general framework for nonholonomic mechanics: Nonholonomic Systems on Lie affgebroids
title_full_unstemmed A general framework for nonholonomic mechanics: Nonholonomic Systems on Lie affgebroids
title_sort A general framework for nonholonomic mechanics: Nonholonomic Systems on Lie affgebroids
dc.creator.none.fl_str_mv Iglesias, David
Marrero, Juan Carlos
Martin de Diego, David
Sosa, Diana
author Iglesias, David
author_facet Iglesias, David
Marrero, Juan Carlos
Martin de Diego, David
Sosa, Diana
author_role author
author2 Marrero, Juan Carlos
Martin de Diego, David
Sosa, Diana
author2_role author
author
author
dc.subject.none.fl_str_mv Lie algebroids
Lie affgebroids
Lagrangian Mechanics
Hamiltonian Mechanics
Nonholonomic mechanics
Lagrange-d’Alembert equations
Projectors
AV-bundles
Aff-Poisson brackets
Non-holonomic brackets
topic Lie algebroids
Lie affgebroids
Lagrangian Mechanics
Hamiltonian Mechanics
Nonholonomic mechanics
Lagrange-d’Alembert equations
Projectors
AV-bundles
Aff-Poisson brackets
Non-holonomic brackets
description 50 pages.-- Pre-print archive.-- PACS: 45.05.+x; 02.20.Sv; 02.40.Hw
publishDate 2007
dc.date.none.fl_str_mv 2007
2007
2007
dc.type.none.fl_str_mv info:eu-repo/semantics/article
http://purl.org/coar/resource_type/c_6501
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10261/2281
url http://hdl.handle.net/10261/2281
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv http://dx.doi.org/10.1063/1.2776845
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv American Institute of Physics
publisher.none.fl_str_mv American Institute of Physics
dc.source.none.fl_str_mv reponame:DIGITAL.CSIC. Repositorio Institucional del CSIC
instname:Consejo Superior de Investigaciones Científicas (CSIC)
instname_str Consejo Superior de Investigaciones Científicas (CSIC)
reponame_str DIGITAL.CSIC. Repositorio Institucional del CSIC
collection DIGITAL.CSIC. Repositorio Institucional del CSIC
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869409741301612544
score 15,81155

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