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Geometric Hamilton-Jacobi theory for nonholonomic dynamical systems

dc.contributor.authorCariñena, José F.
dc.contributor.authorGràcia Sabaté, Francesc Xavier
dc.contributor.authorMarmo, Giuseppe
dc.contributor.authorMartínez, Eduardo
dc.contributor.authorMuñoz Lecanda, Miguel Carlos
dc.contributor.authorRomán Roy, Narciso
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV
dc.date.accessioned2009-09-18T14:36:35Z
dc.date.available2009-09-18T14:36:35Z
dc.date.issued2009-08-14
dc.identifier.urihttp://hdl.handle.net/2117/3052
dc.description.abstractThe geometric formulation of Hamilton--Jacobi theory for systems with nonholonomic constraints is developed, following the ideas of the authors in previous papers. The relation between the solutions of the Hamilton--Jacobi problem with the symplectic structure defined from the Lagrangian function and the constraints is studied. The concept of complete solutions and their relationship with constants of motion, are also studied in detail. Local expressions using quasivelocities are provided. As an example, the nonholonomic free particle is considered.
dc.format.extent22 p.
dc.language.isoeng
dc.rightsAttribution-NoDerivs 3.0 Spain
dc.rights.urihttp://creativecommons.org/licenses/by-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Geometria
dc.subject.lcshDifferential equations
dc.subject.lcshDifferentiable dynamical systems
dc.subject.lcshHamiltonian systems
dc.subject.lcshDynamics
dc.subject.lcshMechanics
dc.subject.lcshLagrangian functions
dc.subject.otherHamilton–Jacobi equation
dc.subject.otherNonholonomic Lagrangian system
dc.subject.otherQuasivelocity
dc.subject.otherSymplectic manifold
dc.subject.otherConstant of motion
dc.subject.otherComplete integral
dc.titleGeometric Hamilton-Jacobi theory for nonholonomic dynamical systems
dc.typeExternal research report
dc.subject.lemacEquacions diferencials ordinàries
dc.subject.lemacSistemes dinàmics diferenciables
dc.subject.lemacHamilton, Sistemes de
dc.subject.lemacPartícules (Física nuclear)
dc.subject.lemacSistemes dinàmics diferenciables
dc.subject.lemacHamilton, Sistemes de
dc.subject.lemacLagrange, Funcions de
dc.contributor.groupUniversitat Politècnica de Catalunya. DGDSA - Geometria Diferencial, Sistemes Dinàmics i Aplicacions
dc.subject.amsClassificació AMS::34 Ordinary differential equations::34A General theory
dc.subject.amsClassificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory
dc.subject.amsClassificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
dc.subject.amsClassificació AMS::70 Mechanics of particles and systems::70F Dynamics of a system of particles, including celestial mechanics
dc.subject.amsClassificació AMS::70 Mechanics of particles and systems::70G General models, approaches, and methods
dc.subject.amsClassificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics
dc.relation.publisherversionhttp://arXiv.org/abs/0908.2453
dc.rights.accessOpen Access
local.personalitzacitaciotrue


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