DSpace Collection:
http://hdl.handle.net/2117/3204
Wed, 16 Apr 2014 11:02:03 GMT2014-04-16T11:02:03Zwebmaster.bupc@upc.eduUniversitat Politècnica de Catalunya. Servei de Biblioteques i DocumentaciónoGeometric Hamilton-Jacobi theory for higher-order autonomous systems
http://hdl.handle.net/2117/22509
Title: Geometric Hamilton-Jacobi theory for higher-order autonomous systems
Authors: Colombo, Leonardo; de León, Manuel; Prieto Martínez, Pedro Daniel; Román Roy, Narciso
Abstract: The geometric framework for the Hamilton-Jacobi theory is used to study this theory in the ambient of higher-order mechanical systems, both in the Lagrangian and Hamiltonian formalisms. Thus, we state the corresponding Hamilton-Jacobi equations in these formalisms and apply our results to analyze some particular physical examples.Thu, 03 Apr 2014 17:26:58 GMThttp://hdl.handle.net/2117/225092014-04-03T17:26:58ZColombo, Leonardo; de León, Manuel; Prieto Martínez, Pedro Daniel; Román Roy, NarcisonoHamilton–Jacobi equation, Higher–order, Lagrangian and Hamiltonian systems, Symplectic geometryThe geometric framework for the Hamilton-Jacobi theory is used to study this theory in the ambient of higher-order mechanical systems, both in the Lagrangian and Hamiltonian formalisms. Thus, we state the corresponding Hamilton-Jacobi equations in these formalisms and apply our results to analyze some particular physical examples.Unified formalism for the generalized kth-order Hamilton-Jacobi problem
http://hdl.handle.net/2117/21964
Title: Unified formalism for the generalized kth-order Hamilton-Jacobi problem
Authors: Colombo, Leonardo; León, Manuel de; Prieto Martínez, Pedro Daniel; Román Roy, Narciso
Abstract: The geometric formulation of the Hamilton-Jacobi theory enables u
s to generalize it to
systems of higher-order ordinary differential equations. In this w
ork we introduce the unified
Lagrangian-Hamiltonian formalism for the geometric Hamilton-Jacob
i theory on higher-order
autonomous dynamical systems described by regular Lagrangian f
unctions.Mon, 10 Mar 2014 13:07:34 GMThttp://hdl.handle.net/2117/219642014-03-10T13:07:34ZColombo, Leonardo; León, Manuel de; Prieto Martínez, Pedro Daniel; Román Roy, NarcisonoThe geometric formulation of the Hamilton-Jacobi theory enables u
s to generalize it to
systems of higher-order ordinary differential equations. In this w
ork we introduce the unified
Lagrangian-Hamiltonian formalism for the geometric Hamilton-Jacob
i theory on higher-order
autonomous dynamical systems described by regular Lagrangian f
unctions.Reduction of polysymplectic manifolds
http://hdl.handle.net/2117/20217
Title: Reduction of polysymplectic manifolds
Authors: Román Roy, Narciso; Marrero González, Juan Carlos; Salgado Seco, Modesto; Vilariño, Silvia
Abstract: The aim of this paper is to generalize the classical Marsden-
Weinstein reduction procedure
for symplectic manifolds to polysymplectic manifolds in or
der to obtain quotient manifolds which in-
herit the polysymplectic structure. This generalization a
llows us to reduce polysymplectic Hamiltonian
systems with symmetries, suuch as those appearing in certai
n kinds of classical field theories. As an
application of this technique, an analogous to the Kirillov
-Kostant-Souriau theorem for polysymplectic
manifolds is obtained and some other mathematical examples
are also analyzed.
Our procedure corrects some mistakes and inaccuracies in pr
evious papers [28, 48] on this subject.Thu, 26 Sep 2013 11:58:32 GMThttp://hdl.handle.net/2117/202172013-09-26T11:58:32ZRomán Roy, Narciso; Marrero González, Juan Carlos; Salgado Seco, Modesto; Vilariño, SilvianoPolysymplectic manifolds, Marsden-Weinstein reduction, k-coadjoint orbits, Polysymplectic Hamiltonian systems.The aim of this paper is to generalize the classical Marsden-
Weinstein reduction procedure
for symplectic manifolds to polysymplectic manifolds in or
der to obtain quotient manifolds which in-
herit the polysymplectic structure. This generalization a
llows us to reduce polysymplectic Hamiltonian
systems with symmetries, suuch as those appearing in certai
n kinds of classical field theories. As an
application of this technique, an analogous to the Kirillov
-Kostant-Souriau theorem for polysymplectic
manifolds is obtained and some other mathematical examples
are also analyzed.
Our procedure corrects some mistakes and inaccuracies in pr
evious papers [28, 48] on this subject.Lagrangian-Hamiltonian unified formalism for autonomous higher-order dynamical systems
http://hdl.handle.net/2117/13114
Title: Lagrangian-Hamiltonian unified formalism for autonomous higher-order dynamical systems
Authors: Prieto Martínez, Pedro Daniel; Román Roy, Narciso
Abstract: Research paperThu, 25 Aug 2011 10:35:53 GMThttp://hdl.handle.net/2117/131142011-08-25T10:35:53ZPrieto Martínez, Pedro Daniel; Román Roy, NarcisonoResearch paperOn a kind of Noether symmetries and conservation laws in k-cosymplectic field theory
http://hdl.handle.net/2117/11508
Title: On a kind of Noether symmetries and conservation laws in k-cosymplectic field theory
Authors: Marrero González, Juan Carlos; Román Roy, Narciso; Salgado, Modesto; Vilariño, Silvia
Abstract: This paper is devoted to studying symmetries of certain kinds of k-cosymplectic Hamiltonian systems in first-order classical field theories. Thus, we introduce a particular class of symmetries and study the problem of associating conservation laws to them by means of a suitable generalization of Noether’s theorem.Wed, 23 Feb 2011 13:26:00 GMThttp://hdl.handle.net/2117/115082011-02-23T13:26:00ZMarrero González, Juan Carlos; Román Roy, Narciso; Salgado, Modesto; Vilariño, SilvianoThis paper is devoted to studying symmetries of certain kinds of k-cosymplectic Hamiltonian systems in first-order classical field theories. Thus, we introduce a particular class of symmetries and study the problem of associating conservation laws to them by means of a suitable generalization of Noether’s theorem.Geometric Hamilton-Jacobi theory for nonholonomic dynamical systems
http://hdl.handle.net/2117/3052
Title: Geometric Hamilton-Jacobi theory for nonholonomic dynamical systems
Authors: Cariñena, José F.; Gràcia Sabaté, Francesc Xavier; Marmo, Giuseppe; Martínez, Eduardo; Muñoz Lecanda, Miguel Carlos; Román Roy, Narciso
Abstract: The 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.Fri, 18 Sep 2009 14:36:35 GMThttp://hdl.handle.net/2117/30522009-09-18T14:36:35ZCariñena, José F.; Gràcia Sabaté, Francesc Xavier; Marmo, Giuseppe; Martínez, Eduardo; Muñoz Lecanda, Miguel Carlos; Román Roy, NarcisonoHamilton–Jacobi equation, Nonholonomic Lagrangian system, Quasivelocity, Symplectic manifold, Constant of motion, Complete integralThe 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.Conservació de l'estructura PHS en reduccions d'ordre per truncament equilibrat
http://hdl.handle.net/2117/1775
Title: Conservació de l'estructura PHS en reduccions d'ordre per truncament equilibrat
Authors: Ras Sabido, AntoniWed, 05 Mar 2008 17:27:27 GMThttp://hdl.handle.net/2117/17752008-03-05T17:27:27ZRas Sabido, AntoninoSistemes dinàmics, Reducció d'ordre, Sistemes hamiltonians