DGDSA  Geometria Diferencial, Sistemes Dinàmics i Aplicacions
http://hdl.handle.net/2117/3202
Mon, 30 Nov 2015 03:09:06 GMT
20151130T03:09:06Z

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.
Wed, 04 Nov 2015 11:07:30 GMT
http://hdl.handle.net/2117/78759
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.
Wed, 23 Sep 2015 13:01:38 GMT
http://hdl.handle.net/2117/77056
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.
Fri, 24 Apr 2015 11:51:21 GMT
http://hdl.handle.net/2117/27582
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.
Wed, 22 Apr 2015 12:16:35 GMT
http://hdl.handle.net/2117/27514
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.
Thu, 03 Apr 2014 17:35:10 GMT
http://hdl.handle.net/2117/22510
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.
Thu, 03 Apr 2014 17:26:58 GMT
http://hdl.handle.net/2117/22509
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.
Mon, 10 Mar 2014 13:07:34 GMT
http://hdl.handle.net/2117/21964
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.
Thu, 26 Sep 2013 11:58:32 GMT
http://hdl.handle.net/2117/20217
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.

Kinematic reduction and the HamiltonJacobi equation
http://hdl.handle.net/2117/19874
Kinematic reduction and the HamiltonJacobi equation
Barbero Liñán, María; De León, Manuel; Martin de Diego, David; Marrero, Juan Carlos; Muñoz Lecanda, Miguel Carlos
A close relationship between the classical Hamilton
Jacobi theory and the kinematic reduction of control systems by
decoupling vector fields is shown in this paper. The geometric interpretation
of this relationship relies on new mathematical techniques
for mechanics defined on a skewsymmetric algebroid. This
geometric structure allows us to describe in a simplified way the
mechanics of nonholonomic systems with both control and external
forces.
Tue, 09 Jul 2013 12:44:47 GMT
http://hdl.handle.net/2117/19874
20130709T12:44:47Z
Barbero Liñán, María
De León, Manuel
Martin de Diego, David
Marrero, Juan Carlos
Muñoz Lecanda, Miguel Carlos
A close relationship between the classical Hamilton
Jacobi theory and the kinematic reduction of control systems by
decoupling vector fields is shown in this paper. The geometric interpretation
of this relationship relies on new mathematical techniques
for mechanics defined on a skewsymmetric algebroid. This
geometric structure allows us to describe in a simplified way the
mechanics of nonholonomic systems with both control and external
forces.

Characterization of accessibility for affine connection control systems at some points with nonzero velocity
http://hdl.handle.net/2117/16211
Characterization of accessibility for affine connection control systems at some points with nonzero velocity
Barbero Liñán, María
Affine connection control systems are mechanical control systems that model a wide range of real systems such as robotic legs, hovercrafts, planar rigid bodies, rolling pennies, snakeboards and so on. In 1997 the accessibility and a particular notion of controllability was intrinsically described by A. D. Lewis and R. Murray at points of zero velocity. Here, we present a novel generalization of the description of accessibility algebra for those systems at some points with nonzero velocity as long as the affine connection restricts to the distribution given by the symmetric closure. The results are used to describe the accessibility algebra of different mechanical control systems
Mon, 09 Jul 2012 14:57:53 GMT
http://hdl.handle.net/2117/16211
20120709T14:57:53Z
Barbero Liñán, María
Affine connection control systems are mechanical control systems that model a wide range of real systems such as robotic legs, hovercrafts, planar rigid bodies, rolling pennies, snakeboards and so on. In 1997 the accessibility and a particular notion of controllability was intrinsically described by A. D. Lewis and R. Murray at points of zero velocity. Here, we present a novel generalization of the description of accessibility algebra for those systems at some points with nonzero velocity as long as the affine connection restricts to the distribution given by the symmetric closure. The results are used to describe the accessibility algebra of different mechanical control systems