114 citations · 578 across the 31 of their papers we have counts for
32 papers
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…
Constrained Lagrangian dissipative contact dynamics
Manuel de León, Manuel Laínz, Miguel C. Muñoz-Lecanda +1
We show that the contact dynamics obtained from the Herglotz variational principle can be described as a constrained nonholonomic or vakonomic ordinary Lagrangian system depending…
Symmetries and gauge symmetries in multisymplectic first and second-order Lagrangian field theories: electromagnetic and gravitational fields
Jordi Gaset, Narciso Román-Roy
Symmetries and, in particular, Cartan (Noether) symmetries and conserved quantities (conservation laws) are studied for the multisymplectic formulation of first and second order La…
The second-order problem for -presymplectic Lagrangian field theories. Application to the Einstein--Palatini model
David Adame-Carrillo, Jordi Gaset, Narciso Román-Roy
In general, the system of nd-order partial differential equations made of the Euler-Lagrange equations of classical field theories are not compatible for singular Lagrangians. T…
An overview of the Hamilton--Jacobi theory: the classical and geometrical approaches and some extensions and applications
Narciso Román-Roy
This work is devoted to review the modern geometric description of the Lagrangian and Hamiltonian formalisms of the Hamilton--Jacobi theory. The relation with the "classical" Hamil…
Higher-order contact mechanics
Manuel de León, Jordi Gaset, Manuel Laínz +2
We present a complete theory of higher-order autonomous contact mechanics, which allows us to describe higher-order dynamical systems with dissipation. The essential tools for the…
Unified Lagrangian-Hamiltonian formalism for contact systems
Manuel de León, Jordi Gaset, Manuel Laínz +2
We present a unified geometric framework for describing both the Lagrangian and Hamiltonian formalisms of contact autonomous mechanical systems, which is based on the approach of t…
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,…
Multisymplectic formulation of Lagrangian models in gravitation
Jordi Gaset, Narciso Román-Roy
We apply the multisymplectic formulation of classical field theories [11, 12, 14] to describe the Einstein-Hilbert and the Einstein-Palatini (or metric-affine) Lagrangian models of…
Griffiths Variational Multisymplectic Formulation for Lovelock Gravity
Santiago Capriotti, Jordi Gaset, Narciso Román-Roy +1
This work is mainly devoted to constructing a multisymplectic description of Lovelock's gravity, which is an extension of General Relativity. We establish a Griffiths variational p…
A contact geometry framework for field theories with dissipation
Jordi Gaset, Xavier Gràcia, Miguel C. Muñoz-Lecanda +2
We develop a new geometric framework suitable for dealing with Hamiltonian field theories with dissipation. To this end we define the notions of -contact structure and -conta…
Constraint algorithm for singular field theories in the -cosymplectic framework
Xavier Gràcia, Xavier Rivas, Narciso Román-Roy
The aim of this paper is to develop a constraint algorithm for singular classical field theories in the framework of -cosymplectic geometry. Since these field theories are singu…
Properties of Multisymplectic Manifolds
Narciso Román-Roy
This lecture is devoted to review some of the main properties of multisymplectic geometry. In particular, after reminding the standard definition of multisymplectic manifold, we in…
A Summary on Symmetries and Conserved Quantities of Autonomous Hamiltonian Systems,
N. Román-Roy
A complete geometric classification of symmetries of autonomous Hamiltonian mechanical systems is established; explaining how to obtain their associated conserved quantities in all…
New multisymplectic approach to the Metric-Affine (Einstein-Palatini) action for gravity
Jordi Gaset, Narciso Román-Roy
We present a covariant multisymplectic formulation for the Einstein-Palatini (or Metric-Affine) model of General Relativity (without energy-matter sources). As it is described by a…
Remarks on multisymplectic reduction
Arturo Echeverría-Enríquez, Miguel C. Muñoz-Lecanda, Narciso Román-Roy
The problem of reduction of multisymplectic manifolds by the action of Lie groups is stated and discussed, as a previous step to give a fully covariant scheme of reduction for clas…
Structural aspects of Hamilton-Jacobi theory
José F. Cariñena, Xavier Gràcia, Giuseppe Marmo +3
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 dy…
Hamilton-Jacobi theory in multisymplectic classical field theories
Manuel de León, Pedro Daniel Prieto-Martínez, Narciso Román-Roy +1
The geometric framework for the Hamilton-Jacobi theory developed in previous works is extended for multisymplectic first-order classical field theories. The Hamilton-Jacobi problem…
Variational Principles for multisymplectic second-order classical field theories
Pedro Daniel Prieto-Martínez, Narciso Román-Roy
We state a unified geometrical version of the variational principles for second-order classical field theories. The standard Lagrangian and Hamiltonian variational principles and t…
A new multisymplectic unified formalism for second-order classical field theories
Pedro D. Prieto-Martínez, Narciso Román-Roy
We present a new multisymplectic framework for second-order classical field theories which is based on an extension of the unified Lagrangian-Hamiltonian formalism to these kinds o…
Unified formalism for the generalized kth-order Hamilton-Jacobi problem
Leonardo Colombo, Manuel de León, Pedro D. Prieto-Martínez +1
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 unifie…
Geometric Hamilton-Jacobi theory for higher-order autonomous systems
Leonardo Colombo, Manuel de León, Pedro Daniel Prieto-Martínez +1
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 formal…
Reduction of polysymplectic manifolds
Juan Carlos Marrero, Narciso Román-Roy, Modesto Salgado +1
The aim of this paper is to generalize the classical Marsden-Weinstein reduction procedure for symplectic manifolds to polysymplectic manifolds in order to obtain quotient manifold…
Higher-order Mechanics: Variational Principles and other topics
Pedro D. Prieto-Martínez, Narciso Román-Roy
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 v…