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Higherorder mechanics: variational principles and other topics
http://hdl.handle.net/2117/22510
Title: Higherorder mechanics: variational principles and other topics
Authors: Prieto Martínez, Pedro Daniel; Román Roy, Narciso
Abstract: 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
no
Higherorder mechanics, Lagrangian and hamiltonian formalisms, Nonautonomous sytems, Skinnerrusk formulation, Variational Principles
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
Title: Geometric HamiltonJacobi theory for higherorder autonomous systems
Authors: Colombo, Leonardo; de León, Manuel; Prieto Martínez, Pedro Daniel; Román Roy, Narciso
Abstract: 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
no
Hamilton–Jacobi equation, Higher–order, Lagrangian and Hamiltonian systems, Symplectic geometry
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
Title: Unified formalism for the generalized kthorder HamiltonJacobi problem
Authors: Colombo, Leonardo; León, Manuel de; Prieto Martínez, Pedro Daniel; Román Roy, Narciso
Abstract: 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
no
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
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
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
no
Polysymplectic manifolds, MarsdenWeinstein reduction, kcoadjoint 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
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
Title: Kinematic reduction and the HamiltonJacobi equation
Authors: Barbero Liñán, María; De León, Manuel; Martin de Diego, David; Marrero, Juan Carlos; Muñoz Lecanda, Miguel Carlos
Abstract: 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
no
Decoupling vector fields, HamiltonJacobi equation, Kinematic reduction, Mechanical control systems, Skewsymmetric algebroids
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
Title: Characterization of accessibility for affine connection control systems at some points with nonzero velocity
Authors: Barbero Liñán, María
Abstract: 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
no
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

Higher education needs for the information and communication technology spanish market
http://hdl.handle.net/2117/14430
Title: Higher education needs for the information and communication technology spanish market
Authors: Llorens García, Ariadna; Llinàs Audet, Francisco Javier; Ras Sabido, Antoni
Abstract: Purpose: The main objective of the paper is to clarify the expectations held in the realm of business and by employers, in relation to the main educational parameters that respond to the employment needs of the Information and Communication Technology (ICT) market in Spain, considering both technical and managerial knowledge. It also assesses whether the Spanish Technical University is providing its graduates with the knowledge currently demanded by the sector. Design/methodology/approach: The report is based on a survey completed by 43 companies, which constitutes more than 60% of the sector and is representative of the entire range of subsectors that constitute the vast ICT industry in Spain. According to the sample construction, poststratification has been used for analyzing global results. Responses have been weighted according to the proportion that represents the employees’ population of the Spanish ICT sector. Findings: As a first conclusion of the current research it should be noted that in terms of technological knowledge, the gap between what the industry requires and the skills graduates can offer is, in general, much smaller than the gap relating to business management skills, where differences exceeding 25% have been demonstrated. This would suggest that the Spanish ICT sector needs to improve learning in the subjects related to business management. Originality/value: Finally, as an innovate factor since there are no previous bibliographic references on this topic, a surprising conclusion is that a significant segment of the Spanish ICT sector, specifically 51,2 % of the companies surveyed, did not distinguish between professional profiles, expressed indifference, and were equally likely to employ graduates as postgraduates. Although when the market was asked about the preferred profile for managerial positions, the results are quite different: 83.7% of respondents preferred a superior engineer qualification; 16.3%
Mon, 09 Jan 2012 14:25:04 GMT
http://hdl.handle.net/2117/14430
20120109T14:25:04Z
Llorens García, Ariadna; Llinàs Audet, Francisco Javier; Ras Sabido, Antoni
no
Purpose: The main objective of the paper is to clarify the expectations held in the realm of business and by employers, in relation to the main educational parameters that respond to the employment needs of the Information and Communication Technology (ICT) market in Spain, considering both technical and managerial knowledge. It also assesses whether the Spanish Technical University is providing its graduates with the knowledge currently demanded by the sector. Design/methodology/approach: The report is based on a survey completed by 43 companies, which constitutes more than 60% of the sector and is representative of the entire range of subsectors that constitute the vast ICT industry in Spain. According to the sample construction, poststratification has been used for analyzing global results. Responses have been weighted according to the proportion that represents the employees’ population of the Spanish ICT sector. Findings: As a first conclusion of the current research it should be noted that in terms of technological knowledge, the gap between what the industry requires and the skills graduates can offer is, in general, much smaller than the gap relating to business management skills, where differences exceeding 25% have been demonstrated. This would suggest that the Spanish ICT sector needs to improve learning in the subjects related to business management. Originality/value: Finally, as an innovate factor since there are no previous bibliographic references on this topic, a surprising conclusion is that a significant segment of the Spanish ICT sector, specifically 51,2 % of the companies surveyed, did not distinguish between professional profiles, expressed indifference, and were equally likely to employ graduates as postgraduates. Although when the market was asked about the preferred profile for managerial positions, the results are quite different: 83.7% of respondents preferred a superior engineer qualification; 16.3%

On a kind of Noether symmetries and conservation laws in kcosymplectic field theory
http://hdl.handle.net/2117/13984
Title: On a kind of Noether symmetries and conservation laws in kcosymplectic 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 kcosymplectic
Hamiltonian systems in firstorder 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.
Mon, 21 Nov 2011 10:52:23 GMT
http://hdl.handle.net/2117/13984
20111121T10:52:23Z
Marrero González, Juan Carlos; Román Roy, Narciso; Salgado, Modesto; Vilariño, Silvia
no
This paper is devoted to studying symmetries of certain kinds of kcosymplectic
Hamiltonian systems in firstorder 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.

On the ksymplectic, kcosymplectic and multisymplectic formalisms of classical field theories
http://hdl.handle.net/2117/13693
Title: On the ksymplectic, kcosymplectic and multisymplectic formalisms of classical field theories
Authors: Román Roy, Narciso; Rey, Angel M.; Salgado, Modesto; Vilariño, Silvia
Abstract: The objective of this work is twofold: First, we analyze the relation between the kcosymplectic and the ksymplectic Hamiltonian and Lagrangian formalisms in classical eld theories. In particular, we prove the equivalence between ksymplectic eld theories and the socalled autonomous kcosymplectic eld theories, extending in this way the description of the symplectic formalism of autonomous systems as a particular case of the cosymplectic formalism in nonautonomous mechanics. Furthermore, we clarify some aspects of the
geometric character of the solutions to the Hamiltonde DonderWeyl and the EulerLagrange equations in these formalisms. Second, we study the equivalence between kcosymplectic and a particular kind of multisymplectic Hamiltonian and Lagrangian eld theories (those where the con guration bundle of the theory is trivial).
Thu, 27 Oct 2011 18:04:04 GMT
http://hdl.handle.net/2117/13693
20111027T18:04:04Z
Román Roy, Narciso; Rey, Angel M.; Salgado, Modesto; Vilariño, Silvia
no
The objective of this work is twofold: First, we analyze the relation between the kcosymplectic and the ksymplectic Hamiltonian and Lagrangian formalisms in classical eld theories. In particular, we prove the equivalence between ksymplectic eld theories and the socalled autonomous kcosymplectic eld theories, extending in this way the description of the symplectic formalism of autonomous systems as a particular case of the cosymplectic formalism in nonautonomous mechanics. Furthermore, we clarify some aspects of the
geometric character of the solutions to the Hamiltonde DonderWeyl and the EulerLagrange equations in these formalisms. Second, we study the equivalence between kcosymplectic and a particular kind of multisymplectic Hamiltonian and Lagrangian eld theories (those where the con guration bundle of the theory is trivial).

LagrangianHamiltonian unified formalism for autonomous higher order dynamical systems
http://hdl.handle.net/2117/13521
Title: LagrangianHamiltonian unified formalism for autonomous higher order dynamical systems
Authors: Prieto Martínez, Pedro Daniel; Román Roy, Narciso
Abstract: The LagrangianHamiltonian unified formalism of R. Skinner and R. Rusk was originally
stated for autonomous dynamical systems in classical mechanics. It has been generalized for
nonautonomous firstorder mechanical systems, as well as for firstorder and higherorder
field theories. However, a complete generalization to higherorder mechanical systems has
yet to be described. In this work, after reviewing the natural geometrical setting and the
Lagrangian and Hamiltonian formalisms for higherorder autonomous mechanical systems,
we develop a complete generalization of the LagrangianHamiltonian unified formalism for
these kinds of systems, and we use it to analyze some physical models from this new point
of view.
Mon, 17 Oct 2011 09:38:13 GMT
http://hdl.handle.net/2117/13521
20111017T09:38:13Z
Prieto Martínez, Pedro Daniel; Román Roy, Narciso
no
The LagrangianHamiltonian unified formalism of R. Skinner and R. Rusk was originally
stated for autonomous dynamical systems in classical mechanics. It has been generalized for
nonautonomous firstorder mechanical systems, as well as for firstorder and higherorder
field theories. However, a complete generalization to higherorder mechanical systems has
yet to be described. In this work, after reviewing the natural geometrical setting and the
Lagrangian and Hamiltonian formalisms for higherorder autonomous mechanical systems,
we develop a complete generalization of the LagrangianHamiltonian unified formalism for
these kinds of systems, and we use it to analyze some physical models from this new point
of view.

LagrangianHamiltonian unified formalism for autonomous higherorder dynamical systems
http://hdl.handle.net/2117/13114
Title: LagrangianHamiltonian unified formalism for autonomous higherorder dynamical systems
Authors: Prieto Martínez, Pedro Daniel; Román Roy, Narciso
Abstract: Research paper
Thu, 25 Aug 2011 10:35:53 GMT
http://hdl.handle.net/2117/13114
20110825T10:35:53Z
Prieto Martínez, Pedro Daniel; Román Roy, Narciso
no
Research paper

The ICT skills gap in Spain: industry expectations versus university preparation
http://hdl.handle.net/2117/11961
Title: The ICT skills gap in Spain: industry expectations versus university preparation
Authors: Llorens García, Ariadna; Llinàs Audet, Francisco Javier; Ras Sabido, Antoni; Chiaramonte Cipolla, Luis Alejandro
Abstract: This article distinguishes which generic skills are the key to enable newly graduated engineers,
basically computer and telecommunication engineers, to enter the information and communication technology
(ICT) sector, satisfying industry demand in Spain. It also demonstrates significant differences between the engineering
degrees (at graduate level) and the engineering master degrees (at postgraduate level) related to skills
needs. Furthermore, this work establishes the fact that there is a gap between the expectations of the ICT sector and
the computerbased engineering curricula and telecommunication engineering curricula the graduated receives,
and where this gap appears in relation to generic competences or skills.
Fri, 18 Mar 2011 13:55:01 GMT
http://hdl.handle.net/2117/11961
20110318T13:55:01Z
Llorens García, Ariadna; Llinàs Audet, Francisco Javier; Ras Sabido, Antoni; Chiaramonte Cipolla, Luis Alejandro
no
computerbased engineering curricula, skills development, information and communication technologies
This article distinguishes which generic skills are the key to enable newly graduated engineers,
basically computer and telecommunication engineers, to enter the information and communication technology
(ICT) sector, satisfying industry demand in Spain. It also demonstrates significant differences between the engineering
degrees (at graduate level) and the engineering master degrees (at postgraduate level) related to skills
needs. Furthermore, this work establishes the fact that there is a gap between the expectations of the ICT sector and
the computerbased engineering curricula and telecommunication engineering curricula the graduated receives,
and where this gap appears in relation to generic competences or skills.

Multisymplectic Lagrangian and Hamiltonian formalisms of classical field theories
http://hdl.handle.net/2117/11879
Title: Multisymplectic Lagrangian and Hamiltonian formalisms of classical field theories
Authors: Román Roy, Narciso
Abstract: This review paper is devoted to presenting the standard multisymplectic formulation
for describing geometrically classical field theories, both the regular and singular cases.
First, the main features of the Lagrangian formalism are revisited and, second, the Hamiltonian formalism is constructed using Hamiltonian sections. In both cases, the variational principles leading to the Euler–Lagrange and the Hamilton–De Donder–Weyl equations, respectively, are stated, and these field equations are given in different but equivalent geometrical ways in each formalism. Finally, both are unified in a new formulation (which has been developed in the last years), following the original ideas of Rusk and Skinner for mechanical systems.
Wed, 16 Mar 2011 13:27:18 GMT
http://hdl.handle.net/2117/11879
20110316T13:27:18Z
Román Roy, Narciso
no
This review paper is devoted to presenting the standard multisymplectic formulation
for describing geometrically classical field theories, both the regular and singular cases.
First, the main features of the Lagrangian formalism are revisited and, second, the Hamiltonian formalism is constructed using Hamiltonian sections. In both cases, the variational principles leading to the Euler–Lagrange and the Hamilton–De Donder–Weyl equations, respectively, are stated, and these field equations are given in different but equivalent geometrical ways in each formalism. Finally, both are unified in a new formulation (which has been developed in the last years), following the original ideas of Rusk and Skinner for mechanical systems.

HamiltonJacobi theory and the evolution operator
http://hdl.handle.net/2117/11524
Title: HamiltonJacobi theory and the evolution operator
Authors: Cariñena Marzo, José Fernando; Gràcia Sabaté, Francesc Xavier; Martínez Fernández, Eduardo; Marmo, Giuseppe; Muñoz Lecanda, Miguel Carlos; Román Roy, Narciso
Abstract: We present a new setting of the geometric HamiltonJacobi theory by using the socalled timeevolution operator K. This new approach unifies both the Lagrangian and
the Hamiltonian formulation of the problem developed in [7], and can be applied to the
case of singular Lagrangian dynamical systems.
Thu, 24 Feb 2011 13:13:13 GMT
http://hdl.handle.net/2117/11524
20110224T13:13:13Z
Cariñena Marzo, José Fernando; Gràcia Sabaté, Francesc Xavier; Martínez Fernández, Eduardo; Marmo, Giuseppe; Muñoz Lecanda, Miguel Carlos; Román Roy, Narciso
no
We present a new setting of the geometric HamiltonJacobi theory by using the socalled timeevolution operator K. This new approach unifies both the Lagrangian and
the Hamiltonian formulation of the problem developed in [7], and can be applied to the
case of singular Lagrangian dynamical systems.

On a kind of Noether symmetries and conservation laws in kcosymplectic field theory
http://hdl.handle.net/2117/11508
Title: On a kind of Noether symmetries and conservation laws in kcosymplectic 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 kcosymplectic Hamiltonian systems in firstorder 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 GMT
http://hdl.handle.net/2117/11508
20110223T13:26:00Z
Marrero González, Juan Carlos; Román Roy, Narciso; Salgado, Modesto; Vilariño, Silvia
no
This paper is devoted to studying symmetries of certain kinds of kcosymplectic Hamiltonian systems in firstorder 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.