Reports de recerca
http://hdl.handle.net/2117/3204
2017-10-23T21:08:32ZHamilton-Jacobi theory in multisymplectic classical field theories
http://hdl.handle.net/2117/81799
Hamilton-Jacobi theory in multisymplectic classical field theories
de León, Manuel; Prieto Martínez, Pedro Daniel; Román Roy, Narciso; Vilariño, Silvia
The geometric framework for the Hamilton-Jacobi theory developed in [14, 17, 39] is extended for multisymplectic first-order classical field theories. The Hamilton-Jacobi problema is stated for the Lagrangian and the Hamiltonian formalisms of these theories as a particular case of a more general problem, and the classical Hamilton-Jacobi equation for field theories is recovered from this geometrical setting. Particular and complete solutions to these problems are defined and characterized in several equivalent ways in both formalisms, and the equivalence between them is proved. The use of distributions in jet bundles that represent
the solutions to the field equations is the fundamental tool in this formulation. Some examples are analyzed and, in particular, the Hamilton-Jacobi equation for non-autonomous mechanical systems is obtained as a special case of our results.
2016-01-21T11:19:16Zde León, ManuelPrieto Martínez, Pedro DanielRomán Roy, NarcisoVilariño, SilviaThe geometric framework for the Hamilton-Jacobi theory developed in [14, 17, 39] is extended for multisymplectic first-order classical field theories. The Hamilton-Jacobi problema is stated for the Lagrangian and the Hamiltonian formalisms of these theories as a particular case of a more general problem, and the classical Hamilton-Jacobi equation for field theories is recovered from this geometrical setting. Particular and complete solutions to these problems are defined and characterized in several equivalent ways in both formalisms, and the equivalence between them is proved. The use of distributions in jet bundles that represent
the solutions to the field equations is the fundamental tool in this formulation. Some examples are analyzed and, in particular, the Hamilton-Jacobi equation for non-autonomous mechanical systems is obtained as a special case of our results.Geometric Hamilton-Jacobi theory for higher-order autonomous systems
http://hdl.handle.net/2117/22509
Geometric Hamilton-Jacobi theory for higher-order autonomous systems
Colombo, Leonardo; de León, Manuel; Prieto Martínez, Pedro Daniel; Román Roy, Narciso
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.
2014-04-03T17:26:58ZColombo, Leonardode León, ManuelPrieto Martínez, Pedro DanielRomán Roy, NarcisoThe 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
Unified formalism for the generalized kth-order Hamilton-Jacobi problem
Colombo, Leonardo; León, Manuel de; Prieto Martínez, Pedro Daniel; Román Roy, Narciso
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.
2014-03-10T13:07:34ZColombo, LeonardoLeón, Manuel dePrieto Martínez, Pedro DanielRomán Roy, NarcisoThe 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
Reduction of polysymplectic manifolds
Román Roy, Narciso; Marrero González, Juan Carlos; Salgado Seco, Modesto; Vilariño, Silvia
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.
2013-09-26T11:58:32ZRomán Roy, NarcisoMarrero González, Juan CarlosSalgado Seco, ModestoVilariño, SilviaThe 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
Lagrangian-Hamiltonian unified formalism for autonomous higher-order dynamical systems
Prieto Martínez, Pedro Daniel; Román Roy, Narciso
Research paper
2011-08-25T10:35:53ZPrieto Martínez, Pedro DanielRomán Roy, NarcisoResearch paperOn a kind of Noether symmetries and conservation laws in k-cosymplectic field theory
http://hdl.handle.net/2117/11508
On a kind of Noether symmetries and conservation laws in k-cosymplectic field theory
Marrero González, Juan Carlos; Román Roy, Narciso; Salgado, Modesto; Vilariño, Silvia
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.
2011-02-23T13:26:00ZMarrero González, Juan CarlosRomán Roy, NarcisoSalgado, ModestoVilariño, SilviaThis 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
Geometric Hamilton-Jacobi theory for nonholonomic dynamical systems
Cariñena, José F.; Gràcia Sabaté, Francesc Xavier; Marmo, Giuseppe; Martínez, Eduardo; Muñoz Lecanda, Miguel Carlos; Román Roy, Narciso
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.
2009-09-18T14:36:35ZCariñena, José F.Gràcia Sabaté, Francesc XavierMarmo, GiuseppeMartínez, EduardoMuñoz Lecanda, Miguel CarlosRomán Roy, NarcisoThe 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
Conservació de l'estructura PHS en reduccions d'ordre per truncament equilibrat
Ras Sabido, Antoni
2008-03-05T17:27:27ZRas Sabido, Antoni