Now showing items 1-15 of 15

  • 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 ...
  • 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 ...
  • 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 ...
  • 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 ...
  • 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
    Restricted access - publisher's policy
    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 ...
  • 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 ...
  • 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; 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 ...
  • 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 ...
  • 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 ...