Now showing items 1-12 of 49

    • Multisymplectic unified formalism for Einstein-Hilbert gravity 

      Gaset Rifà, Jordi; Román Roy, Narciso (2018-03-01)
      Article
      Open Access
      We present a covariant multisymplectic formulation for the Einstein-Hilbert model of General Relativity. As it is described by a second-order singular Lagrangian, this is a gauge field theory with constraints. The use of ...
    • 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 ...
    • The Hamiltonian tube of a cotangent-lifted action 

      Rodríguez Olmos, Miguel Andrés; Teixidó Román, Miguel (2017)
      Article
      Open Access
      The Marle-Guillemin-Sternberg (MGS) form is local model for a neighborhood of an orbit of a Hamiltonian Lie group action on a symplectic manifold. One of the main features of the MGS form is that it puts simultaneously in ...
    • 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, ...
    • Equivalence between the Hamiltonian and Lagrangian formalisms for constrained systems 

      Batlle Arnau, Carles; Gomis Torné, Joaquin; Pons Ràfols, Josep Maria; Román Roy, Narciso (1986-08)
      Article
      Open Access
      The equivalence between the Lagrangian and Hamiltonian formalism is studied for constraint systems. A procedure to construct the Lagrangian constraints from the Hamiltonian constraints is given. Those Hamiltonian constraints ...
    • Structural aspects of Hamilton–Jacobi theory 

      Cariñena Marzo, José F.; Gràcia Sabaté, Francesc Xavier; Marmo, Giuseppe; Martínez Fernandez, Eduardo; Muñoz Lecanda, Miguel Carlos; Román Roy, Narciso (2016-02-01)
      Article
      Open Access
      In our previous papers [11, 13] we showed that the Hamilton–Jacobi problem can be regarded as a way to describe a given dynamics on a phase space manifold in terms of a family of dynamics on a lower-dimensional manifold. ...
    • 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 ...
    • The wave equation for stiff strings and piano tuning 

      Gràcia Sabaté, Francesc Xavier; Sanz Perela, Tomás (2017)
      Article
      Open Access
      We study the wave equation for a string with stiffness. We solve the equation and provide a uniqueness theorem with suitable boundary conditions. For a pinned string we compute the spectrum, which is slightly inharmonic. ...
    • Order reduction, projectability and constrainsts of second-order field theories and higuer-order mechanics 

      Gaset Rifà, Jordi; Román Roy, Narciso (2016-12-01)
      Article
      Open Access
      The consequences of the projectability of Poincar\'e-Cartan forms in a third-order jet bundle $J^3\pi$ to a lower-order jet bundle are analyzed using the constraint algorithm for the Euler-Lagrange equations in $J^3\pi$. ...
    • A Hamiltonian study of the stability and bifurcations for the satellite problem 

      Muñoz Lecanda, Miguel Carlos; Rodríguez Olmos, Miguel Andrés; Teixidó Román, Miguel (2015-10-01)
      Article
      Open Access
      We study the dynamics of a rigid body in a central gravitational field modeled as a Hamiltonian system with continuous rotational symmetries following the geometric framework of Wang et al. Novelties of our work are the ...
    • Classification and stability of relative equilibria for the two-body problem in the hyperbolic space of dimension 2 

      García Naranjo Ortiz de la Huerta, Luis Constantino; Marrero, Juan Carlos; Perez Chavela, Ernesto; Rodríguez Olmos, Miguel Andrés (2016-01-13)
      Article
      Open Access
      We classify and analyze the stability of all relative equilibria for the two-body problem in the hyperbolic space of dimension 2 and we formulate our results in terms of the intrinsic Riemannian data of the problem.
    • Music and mathematics. From Pythagoras to fractals 

      Gràcia Sabaté, Francesc Xavier (2015-12-30)
      Article
      Open Access