Working papers
http://hdl.handle.net/2117/5947
2023-06-03T14:11:11ZUnified formalism for non-autonomous mechanical systems
http://hdl.handle.net/2117/2654
Unified formalism for non-autonomous mechanical systems
Barbero Liñán, María; Echeverría Enríquez, Arturo; Martín de Diego, David; Muñoz Lecanda, Miguel Carlos; Román Roy, Narciso
We present a unified geometric framework for describing both the Lagrangian and Hamiltonian formalisms of regular and non-regular time-dependent mechanical systems, which is based on the approach of Skinner and Rusk (1983). The dynamical equations of motion and their compatibility and consistency are carefully studied, making clear that all the characteristics of the Lagrangian and the Hamiltonian formalisms are recovered in this formulation. As an example, it is studied a semidiscretization of the nonlinear wave equation proving the applicability of the proposed formalism.
2009-03-12T16:12:54ZBarbero Liñán, MaríaEcheverría Enríquez, ArturoMartín de Diego, DavidMuñoz Lecanda, Miguel CarlosRomán Roy, NarcisoWe present a unified geometric framework for describing both the Lagrangian and Hamiltonian formalisms of regular and non-regular time-dependent mechanical systems, which is based on the approach of Skinner and Rusk (1983). The dynamical equations of motion and their compatibility and consistency are carefully studied, making clear that all the characteristics of the Lagrangian and the Hamiltonian formalisms are recovered in this formulation. As an example, it is studied a semidiscretization of the nonlinear wave equation proving the applicability of the proposed formalism.Constraint algorithm for k-presymplectic Hamiltonian systems. Application to singular field theories
http://hdl.handle.net/2117/2644
Constraint algorithm for k-presymplectic Hamiltonian systems. Application to singular field theories
Gràcia Sabaté, Francesc Xavier; Martín Grillo, Rubén; Román Roy, Narciso
The k-symplectic formulation of field theories is especially simple, since only tangent and cotangent bundles are needed in its description. Its defining elements show a close relationship with those in the symplectic formulation of mechanics. It will be shown that this relationship also stands in the presymplectic case. In a natural way,
one can mimick the presymplectic constraint algorithm to obtain a constraint algorithm
that can be applied to k-presymplectic field theory, and more particularly to the Lagrangian and Hamiltonian formulations of
field theories defined by a singular Lagrangian, as well as to the unified Lagrangian-Hamiltonian formalism (Skinner--Rusk formalism) for k-presymplectic field theory. Two examples of application of the algorithm are also analyzed.
2009-03-10T17:17:19ZGràcia Sabaté, Francesc XavierMartín Grillo, RubénRomán Roy, NarcisoThe k-symplectic formulation of field theories is especially simple, since only tangent and cotangent bundles are needed in its description. Its defining elements show a close relationship with those in the symplectic formulation of mechanics. It will be shown that this relationship also stands in the presymplectic case. In a natural way,
one can mimick the presymplectic constraint algorithm to obtain a constraint algorithm
that can be applied to k-presymplectic field theory, and more particularly to the Lagrangian and Hamiltonian formulations of
field theories defined by a singular Lagrangian, as well as to the unified Lagrangian-Hamiltonian formalism (Skinner--Rusk formalism) for k-presymplectic field theory. Two examples of application of the algorithm are also analyzed.