• 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
      Accés restringit per política de l'editorial
      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 mechanics and Hamilton-Jacobi theory 

      Urtiaga Erneta, Iñigo (Universitat Politècnica de Catalunya, 2017-01)
      Treball Final de Grau
      Accés obert
      A review of analytical mechanics in the language of differential geometry is given. The classical formulations of Newton, Lagrange and Hamilton are discussed in detail, with special interest in the Hamilton-Jacobi equation. ...
    • Kinematic reduction and the Hamilton-Jacobi equation 

      Barbero Liñán, María; De León, Manuel; Martin de Diego, David; Marrero, Juan Carlos; Muñoz Lecanda, Miguel Carlos (American Institute of Mathematical Sciences, 2012)
      Article
      Accés obert
      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 ...
    • 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
      Accés obert
      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. ...
    • 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
      Accés obert
      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 ...