Now showing items 1-16 of 16

    • A new multisymplectic unified formalism for second order classical field theories 

      Prieto Martínez, Pedro Daniel; Román Roy, Narciso (American Institute of Mathematical Sciences, 2015-06-01)
      Article
      Open Access
      We present a new multisymplectic framework for second-order classical field theories which is based on an extension of the unified LagrangianHamiltonian formalism to these kinds of systems. This model provides a straightforward ...
    • Àlgebra lineal : exercicis i problemes comentats 

      Martí Farré, Jaume; Prieto Martínez, Pedro Daniel; Tura, Jordi (Universitat Politècnica de Catalunya, 2012)
      Problem statement, exercise
      Open Access
    • Estudi de les estructures geomètriques dels sistemes dinàmics d'ordre superior 

      Prieto Martínez, Pedro Daniel (Universitat Politècnica de Catalunya, 2011)
      Master thesis
      Open Access
      El formalisme unificat Lagrangià-Hamiltonià de R. Skinner i R. Rusk fou desenvolupat originalment per a sistemes dinàmics autònoms de la mecànica clàssica. Més recentment s'ha generalitzat per a sistemes mecànics no autònoms ...
    • Geometric Hamilton-Jacobi theory for higher-order autonomous systems 

      Colombo, Leonardo; De León, Manuel; Prieto Martínez, Pedro Daniel; Román Roy, Narciso (2014-06-13)
      Article
      Restricted access - publisher's policy
      The geometric framework for the Hamilton-Jacobi theory is used to study this theory in the background of higher-order mechanical systems, in both the Lagrangian and Hamiltonian formalisms. Thus, we state the corresponding ...
    • Geometric Hamilton-Jacobi theory for higher-order autonomous systems 

      Colombo, Leonardo; de León, Manuel; Prieto Martínez, Pedro Daniel; Román Roy, Narciso (2013-09-09)
      External research report
      Open Access
      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 ...
    • Geometrical structures of higher-order dynamical systems and field theories 

      Prieto Martínez, Pedro Daniel (Universitat Politècnica de Catalunya, 2014-10-02)
      Doctoral thesis
      Open Access
      Geometrical physics is a relatively young branch of applied mathematics that was initiated by the 60's and the 70's when A. Lichnerowicz, W.M. Tulczyjew and J.M. Souriau, among many others, began to study various topics ...
    • Hamilton-Jacobi theory in multisymplectic classical field theories 

      de León, Manuel; Prieto Martínez, Pedro Daniel; Román Roy, Narciso; Vilariño, Silvia (2015-04-08)
      External research report
      Open Access
      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 ...
    • Hamilton-Jacobi theory in multisymplectic classical field theories 

      De León, Manuel; Prieto Martínez, Pedro Daniel; Román Roy, Narciso; Vilariño Fernández, Silvia (2017-09-01)
      Article
      Open Access
      The geometric framework for the Hamilton-Jacobi theory developed in the studies of Carinena et al. [Int. J. Geom. Methods Mod. Phys. 3(7), 1417-1458 (2006)], Carinena et al. [Int. J. Geom. Methods Mod. Phys. 13(2), 1650017 ...
    • Higher-order mechanics: variational principles and other topics 

      Prieto Martínez, Pedro Daniel; Román Roy, Narciso (American Institute of Mathematical Sciences, 2013-12)
      Article
      Open Access
      After reviewing the Lagrangian-Hamiltonian unified formalism (i.e, the Skinner-Rusk formalism) for higher-order (non-autonomous) dynamical systems, we state a unified geometrical version of the Variational Principles which ...
    • Lagrangian-Hamiltonian unified formalism for autonomous higher order dynamical systems 

      Prieto Martínez, Pedro Daniel; Román Roy, Narciso (2011-09-23)
      Article
      Restricted access - confidentiality agreement
      The Lagrangian-Hamiltonian unified formalism of R. Skinner and R. Rusk was originally stated for autonomous dynamical systems in classical mechanics. It has been generalized for non-autonomous first-order mechanical ...
    • Lagrangian-Hamiltonian unified formalism for autonomous higher-order dynamical systems 

      Prieto Martínez, Pedro Daniel; Román Roy, Narciso (2011-07-18)
      External research report
      Restricted access - confidentiality agreement
      Research paper
    • Regularity properties of fiber derivatives associated with higher-order mechanical systems 

      Colombo, Leonardo; Prieto Martínez, Pedro Daniel (2016-08)
      Article
      Open Access
      The aim of this work is to study fiber derivatives associated to Lagrangian and Hamiltonian functions describing the dynamics of a higher-order autonomous dynamical system. More precisely, given a function in T*T(k-1)Q, ...
    • Unified formalism for the generalized kth-order Hamilton-Jacobi problem 

      Colombo, Leonardo; De León, Manuel; Prieto Martínez, Pedro Daniel; Román Roy, Narciso (2014-10-01)
      Article
      Open Access
      The geometric formulation of the Hamilton-Jacobi theory enables us to generalize it to systems of higher-order ordinary differential equations. In this work we introduce the unified Lagrangian-Hamiltonian formalism for the ...
    • Unified formalism for the generalized kth-order Hamilton-Jacobi problem 

      Colombo, Leonardo; León, Manuel de; Prieto Martínez, Pedro Daniel; Román Roy, Narciso (2013-10-03)
      External research report
      Open Access
      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 ...
    • Variational principles and symmetries on fibered multisymplectic manifolds 

      Gaset Rifà, Jordi; Prieto Martínez, Pedro Daniel; Román Roy, Narciso (2016-12-01)
      Article
      Open Access
      The standard techniques of variational calculus are geometrically stated in the ambient of fiber bundles endowed with a (pre)multi-symplectic structure. Then, for the corresponding variational equations, conserved quantities ...
    • Variational principles for multisymplectic second-order classical field theories 

      Román Roy, Narciso; Prieto Martínez, Pedro Daniel (2015-09-01)
      Article
      Open Access
      We state a unified geometrical version of the variational principles for second-order classical field theories. The standard Lagrangian and Hamiltonian variational principles and the corresponding field equations are ...