67 citations · 330 across the 21 of their papers we have counts for
23 papers
On Darboux theorems for geometric structures induced by closed forms
Xavier Gràcia, Javier de Lucas, Xavier Rivas +1
This work reviews the classical Darboux theorem for symplectic, presymplectic, and cosymplectic manifolds (which are used to describe regular and singular mechanical systems), and…
Time-dependent contact mechanics
Manuel de León, Jordi Gaset, Xavier Gràcia +2
Contact geometry allows to describe some thermodynamic and dissipative systems. In this paper we introduce a new geometric structure in order to describe time-dependent contact sys…
Reduction and reconstruction of multisymplectic Lie systems
Javier de Lucas, Xavier Gràcia, Xavier Rivas +2
A Lie system is a non-autonomous system of first-order ordinary differential equations describing the integral curves of a non-autonomous vector field taking values in a finite-dim…
Skinner-Rusk formalism for k-contact systems
Xavier Gràcia, Xavier Rivas, Narciso Román-Roy
In previous papers, a geometric framework has been developed to describe non-conservative field theories as a kind of modified Lagrangian and Hamiltonian field theories. This appro…
A -contact Lagrangian formulation for nonconservative field theories
Jordi Gaset, Xavier Gràcia, Miguel C. Muñoz-Lecanda +2
We present a geometric Lagrangian formulation for first-order field theories with dissipation. This formulation is based on the -contact geometry introduced in a previous paper,…
New contributions to the Hamiltonian and Lagrangian contact formalisms for dissipative mechanical systems and their symmetries
Jordi Gaset, Xavier Gràcia, Miguel C. Muñoz-Lecanda +2
We provide new insights into the contact Hamiltonian and Lagrangian formulations of dissipative mechanical systems. In particular, we state a new form of the contact dynamical equa…