Unified formalism for non-autonomous mechanical systems

We present a unified geometric framework for describing both the Lagrangian and Hamiltonian formalisms of regular and non-regular time-dependent mechanical systems, which is based on the approach of Skinner and Rusk (1983). The dynamical equations of motion and their compatibility and consistency ar...

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Autores: Barbero Liñán, María, Echeverría Enríquez, Arturo, Martín de Diego, David, Muñoz Lecanda, Miguel Carlos|||0000-0002-7037-0248, Román Roy, Narciso|||0000-0003-3663-9861
Tipo de recurso: artículo
Fecha de publicación:2008
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:2117/1926
Acceso en línea:https://hdl.handle.net/2117/1926
Access Level:acceso abierto
Palabra clave:Lagrangian functions
Symplectic manifolds
Hamiltonian systems
Lagrangian and Hamiltonian formalisms
Autonomous mechanics
Symplectic and presymplectic manifolds
Lagrange, Funcions de
Hamilton, Sistemes de
Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
Classificació AMS::53 Differential geometry::53D Symplectic geometry, contact geometry
Classificació AMS::55 Algebraic topology::55R Fiber spaces and bundles
Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics
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spelling Unified formalism for non-autonomous mechanical systemsBarbero Liñán, MaríaEcheverría Enríquez, ArturoMartín de Diego, DavidMuñoz Lecanda, Miguel Carlos|||0000-0002-7037-0248Román Roy, Narciso|||0000-0003-3663-9861Lagrangian functionsSymplectic manifoldsHamiltonian systemsLagrangian and Hamiltonian formalismsAutonomous mechanicsSymplectic and presymplectic manifoldsLagrange, Funcions deHamilton, Sistemes deClassificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systemsClassificació AMS::53 Differential geometry::53D Symplectic geometry, contact geometryClassificació AMS::55 Algebraic topology::55R Fiber spaces and bundlesClassificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanicsWe present a unified geometric framework for describing both the Lagrangian and Hamiltonian formalisms of regular and non-regular time-dependent mechanical systems, which is based on the approach of Skinner and Rusk (1983). The dynamical equations of motion and their compatibility and consistency are carefully studied, making clear that all the characteristics of the Lagrangian and the Hamiltonian formalisms are recovered in this formulation. As an example, it is studied a semidiscretization of the nonlinear wave equation proving the applicability of the proposed formalism.20082008-02-2920082008-04-01journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/1926reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivs 2.5 Spainhttp://creativecommons.org/licenses/by-nc-nd/2.5/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/19262026-05-27T15:37:01Z
dc.title.none.fl_str_mv Unified formalism for non-autonomous mechanical systems
title Unified formalism for non-autonomous mechanical systems
spellingShingle Unified formalism for non-autonomous mechanical systems
Barbero Liñán, María
Lagrangian functions
Symplectic manifolds
Hamiltonian systems
Lagrangian and Hamiltonian formalisms
Autonomous mechanics
Symplectic and presymplectic manifolds
Lagrange, Funcions de
Hamilton, Sistemes de
Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
Classificació AMS::53 Differential geometry::53D Symplectic geometry, contact geometry
Classificació AMS::55 Algebraic topology::55R Fiber spaces and bundles
Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics
title_short Unified formalism for non-autonomous mechanical systems
title_full Unified formalism for non-autonomous mechanical systems
title_fullStr Unified formalism for non-autonomous mechanical systems
title_full_unstemmed Unified formalism for non-autonomous mechanical systems
title_sort Unified formalism for non-autonomous mechanical systems
dc.creator.none.fl_str_mv Barbero Liñán, María
Echeverría Enríquez, Arturo
Martín de Diego, David
Muñoz Lecanda, Miguel Carlos|||0000-0002-7037-0248
Román Roy, Narciso|||0000-0003-3663-9861
author Barbero Liñán, María
author_facet Barbero Liñán, María
Echeverría Enríquez, Arturo
Martín de Diego, David
Muñoz Lecanda, Miguel Carlos|||0000-0002-7037-0248
Román Roy, Narciso|||0000-0003-3663-9861
author_role author
author2 Echeverría Enríquez, Arturo
Martín de Diego, David
Muñoz Lecanda, Miguel Carlos|||0000-0002-7037-0248
Román Roy, Narciso|||0000-0003-3663-9861
author2_role author
author
author
author
dc.subject.none.fl_str_mv Lagrangian functions
Symplectic manifolds
Hamiltonian systems
Lagrangian and Hamiltonian formalisms
Autonomous mechanics
Symplectic and presymplectic manifolds
Lagrange, Funcions de
Hamilton, Sistemes de
Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
Classificació AMS::53 Differential geometry::53D Symplectic geometry, contact geometry
Classificació AMS::55 Algebraic topology::55R Fiber spaces and bundles
Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics
topic Lagrangian functions
Symplectic manifolds
Hamiltonian systems
Lagrangian and Hamiltonian formalisms
Autonomous mechanics
Symplectic and presymplectic manifolds
Lagrange, Funcions de
Hamilton, Sistemes de
Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
Classificació AMS::53 Differential geometry::53D Symplectic geometry, contact geometry
Classificació AMS::55 Algebraic topology::55R Fiber spaces and bundles
Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics
description We present a unified geometric framework for describing both the Lagrangian and Hamiltonian formalisms of regular and non-regular time-dependent mechanical systems, which is based on the approach of Skinner and Rusk (1983). The dynamical equations of motion and their compatibility and consistency are carefully studied, making clear that all the characteristics of the Lagrangian and the Hamiltonian formalisms are recovered in this formulation. As an example, it is studied a semidiscretization of the nonlinear wave equation proving the applicability of the proposed formalism.
publishDate 2008
dc.date.none.fl_str_mv 2008
2008-02-29
2008
2008-04-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/1926
url https://hdl.handle.net/2117/1926
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 2.5 Spain
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
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
Attribution-NonCommercial-NoDerivs 2.5 Spain
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
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_ 1869407689031811072
score 15,300719

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