DGDSA  Geometria Diferencial, Sistemes Dinàmics i Aplicacions
http://hdl.handle.net/2117/3202
20160214T10:44:19Z

A new multisymplectic unified formalism for second order classical field theories
http://hdl.handle.net/2117/81889
A new multisymplectic unified formalism for second order classical field theories
Prieto Martínez, Pedro Daniel; Román Roy, Narciso
We present a new multisymplectic framework for secondorder classical field theories which is based on an extension of the unified LagrangianHamiltonian formalism to these kinds of systems. This model provides a straightforward and simple way to define the PoincareCartan form and clarifies the construction of the Legendre map (univocally obtained as a consequence of the constraint algorithm). Likewise, it removes the undesirable arbitrariness in the solutions to the field equations, which are analyzed indepth, and written in terms of holonomic sections and multivector fields. Our treatment therefore completes previous attempt to achieve this aim. The formulation is applied to describing some physical examples; in particular, to giving another alternative multisymplectic description of the Kortewegde Vries equation.
20160122T12:29:06Z
Prieto Martínez, Pedro Daniel
Román Roy, Narciso
We present a new multisymplectic framework for secondorder classical field theories which is based on an extension of the unified LagrangianHamiltonian formalism to these kinds of systems. This model provides a straightforward and simple way to define the PoincareCartan form and clarifies the construction of the Legendre map (univocally obtained as a consequence of the constraint algorithm). Likewise, it removes the undesirable arbitrariness in the solutions to the field equations, which are analyzed indepth, and written in terms of holonomic sections and multivector fields. Our treatment therefore completes previous attempt to achieve this aim. The formulation is applied to describing some physical examples; in particular, to giving another alternative multisymplectic description of the Kortewegde Vries equation.

HamiltonJacobi theory in multisymplectic classical field theories
http://hdl.handle.net/2117/81799
HamiltonJacobi theory in multisymplectic classical field theories
de León, Manuel; Prieto Martínez, Pedro Daniel; Román Roy, Narciso; Vilariño, Silvia
The geometric framework for the HamiltonJacobi theory developed in [14, 17, 39] is extended for multisymplectic firstorder classical field theories. The HamiltonJacobi 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 HamiltonJacobi 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 HamiltonJacobi equation for nonautonomous mechanical systems is obtained as a special case of our results.
20160121T11:19:16Z
de León, Manuel
Prieto Martínez, Pedro Daniel
Román Roy, Narciso
Vilariño, Silvia
The geometric framework for the HamiltonJacobi theory developed in [14, 17, 39] is extended for multisymplectic firstorder classical field theories. The HamiltonJacobi 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 HamiltonJacobi 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 HamiltonJacobi equation for nonautonomous mechanical systems is obtained as a special case of our results.

Variational principles for multisymplectic secondorder classical field theories
http://hdl.handle.net/2117/78759
Variational principles for multisymplectic secondorder classical field theories
Román Roy, Narciso; Prieto Martínez, Pedro Daniel
We state a unified geometrical version of the variational principles for secondorder classical field theories. The standard Lagrangian and Hamiltonian variational principles and the corresponding field equations are recovered from this unified framework.
20151104T11:07:30Z
Román Roy, Narciso
Prieto Martínez, Pedro Daniel
We state a unified geometrical version of the variational principles for secondorder classical field theories. The standard Lagrangian and Hamiltonian variational principles and the corresponding field equations are recovered from this unified framework.

Reduction of polysymplectic manifolds
http://hdl.handle.net/2117/77056
Reduction of polysymplectic manifolds
Marrero, Juan Carlos; Román Roy, Narciso; Salgado Seco, Modesto; Vilariño, Silvia
The aim of this paper is to generalize the classical MarsdenWeinstein reduction procedure for symplectic manifolds to polysymplectic manifolds in order to obtain quotient manifolds which inherit the polysymplectic structure. This generalization allows us to reduce polysymplectic Hamiltonian systems with symmetries, such as those appearing in certain kinds of classical field theories. As an application of this technique, an analogue to the KirillovKostant Souriau theorem for polysymplectic manifolds is obtained and some other mathematical examples are also analyzed. Our procedure corrects some mistakes and inaccuracies in previous papers (Gunther 1987 J. Differ. Geom. 25 2353; Munteanu et al 2004 J. Math. Phys. 45 173051) on this subject.
20150923T13:01:38Z
Marrero, Juan Carlos
Román Roy, Narciso
Salgado Seco, Modesto
Vilariño, Silvia
The aim of this paper is to generalize the classical MarsdenWeinstein reduction procedure for symplectic manifolds to polysymplectic manifolds in order to obtain quotient manifolds which inherit the polysymplectic structure. This generalization allows us to reduce polysymplectic Hamiltonian systems with symmetries, such as those appearing in certain kinds of classical field theories. As an application of this technique, an analogue to the KirillovKostant Souriau theorem for polysymplectic manifolds is obtained and some other mathematical examples are also analyzed. Our procedure corrects some mistakes and inaccuracies in previous papers (Gunther 1987 J. Differ. Geom. 25 2353; Munteanu et al 2004 J. Math. Phys. 45 173051) on this subject.

Unified formalism for the generalized kthorder HamiltonJacobi problem
http://hdl.handle.net/2117/27582
Unified formalism for the generalized kthorder HamiltonJacobi problem
Colombo, Leonardo; De León, Manuel; Prieto Martínez, Pedro Daniel; Román Roy, Narciso
The geometric formulation of the HamiltonJacobi theory enables us to generalize it to systems of higherorder ordinary differential equations. In this work we introduce the unified LagrangianHamiltonian formalism for the geometric HamiltonJacobi theory on higherorder autonomous dynamical systems described by regular Lagrangian functions.
20150424T11:51:21Z
Colombo, Leonardo
De León, Manuel
Prieto Martínez, Pedro Daniel
Román Roy, Narciso
The geometric formulation of the HamiltonJacobi theory enables us to generalize it to systems of higherorder ordinary differential equations. In this work we introduce the unified LagrangianHamiltonian formalism for the geometric HamiltonJacobi theory on higherorder autonomous dynamical systems described by regular Lagrangian functions.

Geometric HamiltonJacobi theory for higherorder autonomous systems
http://hdl.handle.net/2117/27514
Geometric HamiltonJacobi theory for higherorder autonomous systems
Colombo, Leonardo; De León, Manuel; Prieto Martínez, Pedro Daniel; Román Roy, Narciso
The geometric framework for the HamiltonJacobi theory is used to study this theory in the background of higherorder mechanical systems, in both the Lagrangian and Hamiltonian formalisms. Thus, we state the corresponding HamiltonJacobi equations in these formalisms and apply our results to analyze some particular physical examples.
20150422T12:16:35Z
Colombo, Leonardo
De León, Manuel
Prieto Martínez, Pedro Daniel
Román Roy, Narciso
The geometric framework for the HamiltonJacobi theory is used to study this theory in the background of higherorder mechanical systems, in both the Lagrangian and Hamiltonian formalisms. Thus, we state the corresponding HamiltonJacobi equations in these formalisms and apply our results to analyze some particular physical examples.

Higherorder mechanics: variational principles and other topics
http://hdl.handle.net/2117/22510
Higherorder mechanics: variational principles and other topics
Prieto Martínez, Pedro Daniel; Román Roy, Narciso
After reviewing the LagrangianHamiltonian unified formalism (i.e, the SkinnerRusk formalism) for higherorder (nonautonomous) dynamical systems, we state a unified geometrical version of the Variational Principles which allows us to derive the Lagrangian and Hamiltonian equations for these kinds of systems. Then, the standard Lagrangian and Hamiltonian formulations of these principles and the corresponding dynamical equations are recovered from this unified framework.. © American Institute of Mathematical Sciences.
20140403T17:35:10Z
Prieto Martínez, Pedro Daniel
Román Roy, Narciso
After reviewing the LagrangianHamiltonian unified formalism (i.e, the SkinnerRusk formalism) for higherorder (nonautonomous) dynamical systems, we state a unified geometrical version of the Variational Principles which allows us to derive the Lagrangian and Hamiltonian equations for these kinds of systems. Then, the standard Lagrangian and Hamiltonian formulations of these principles and the corresponding dynamical equations are recovered from this unified framework.. © American Institute of Mathematical Sciences.

Geometric HamiltonJacobi theory for higherorder autonomous systems
http://hdl.handle.net/2117/22509
Geometric HamiltonJacobi theory for higherorder autonomous systems
Colombo, Leonardo; de León, Manuel; Prieto Martínez, Pedro Daniel; Román Roy, Narciso
The geometric framework for the HamiltonJacobi theory is used to study this theory in the ambient of higherorder mechanical systems, both in the Lagrangian and Hamiltonian formalisms. Thus, we state the corresponding HamiltonJacobi equations in these formalisms and apply our results to analyze some particular physical examples.
20140403T17:26:58Z
Colombo, Leonardo
de León, Manuel
Prieto Martínez, Pedro Daniel
Román Roy, Narciso
The geometric framework for the HamiltonJacobi theory is used to study this theory in the ambient of higherorder mechanical systems, both in the Lagrangian and Hamiltonian formalisms. Thus, we state the corresponding HamiltonJacobi equations in these formalisms and apply our results to analyze some particular physical examples.

Unified formalism for the generalized kthorder HamiltonJacobi problem
http://hdl.handle.net/2117/21964
Unified formalism for the generalized kthorder HamiltonJacobi problem
Colombo, Leonardo; León, Manuel de; Prieto Martínez, Pedro Daniel; Román Roy, Narciso
The geometric formulation of the HamiltonJacobi theory enables u
s to generalize it to
systems of higherorder ordinary differential equations. In this w
ork we introduce the unified
LagrangianHamiltonian formalism for the geometric HamiltonJacob
i theory on higherorder
autonomous dynamical systems described by regular Lagrangian f
unctions.
20140310T13:07:34Z
Colombo, Leonardo
León, Manuel de
Prieto Martínez, Pedro Daniel
Román Roy, Narciso
The geometric formulation of the HamiltonJacobi theory enables u
s to generalize it to
systems of higherorder ordinary differential equations. In this w
ork we introduce the unified
LagrangianHamiltonian formalism for the geometric HamiltonJacob
i theory on higherorder
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
KostantSouriau 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.
20130926T11:58:32Z
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
KostantSouriau 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.