103 citations · 717 across the 28 of their papers we have counts for
29 papers
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…
Multisymplectic unified formalism for Einstein-Hilbert Gravity
Jordi Gaset, Narciso Román-Roy
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 f…
Variational principles and symmetries on fibered multisymplectic manifolds
Jordi Gaset, Pedro D. Prieto-Martínez, Narciso Román-Roy
The standard techniques of variational calculus are geometrically stated in the ambient of fiber bundles endowed with a (pre)multisymplectic structure. Then, for the corresponding…
Order reduction, projectability and constraints of second-order field theories and higher-order mechanics
Jordi Gaset, Narciso Román-Roy
The projectability of Poincaré-Cartan forms in a third-order jet bundle onto a lower-order jet bundle is a consequence of the degenerate character of the corresponding Lagra…
SOPDEs and Nonlinear Connections
N. Román-Roy, M. Salgado, S. Vilariño
The canonical k-tangent structure on allows us to characterize nonlinear connections on and to develop Günther's (k-symplectic) L…
On a kind of Noether symmetries and conservation laws in k-cosymplectic field theory
J. C. Marrero, N. Román-Roy, M. Salgado +1
This paper is devoted to studying symmetries of certain kinds of k-cosymplectic Hamiltonian systems in first-order classical field theories. Thus, we introduce a particular class o…
Geometric Hamilton-Jacobi Theory for Nonholonomic Dynamical Systems
J. F. Cariñena, X. Gracia, G. Marmo +3
The geometric formulation of Hamilton--Jacobi theory for systems with nonholonomic constraints is developed, following the ideas of the authors in previous papers. The relation bet…
Hamilton-Jacobi theory and the evolution operator
J. F. Carinena, X. Gracia, E. Martinez +3
We present a new setting of the geometric Hamilton-Jacobi theory by using the so-called time-evolution operator K. This new approach unifies both the Lagrangian and the Hamiltonian…
Constraint algorithm for k-presymplectic Hamiltonian systems. Application to singular field theories
Xavier Gracia, Ruben Martin, Narciso Roman-Roy
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 rela…
Higher-order Cartan symmetries in k-symplectic field theory
Narciso Roman-Roy, Modesto Salgado, Silvia Vilarino
For k-symplectic Hamiltonian field theories, we study infinitesimal transformations generated by certain kinds of vector fields which are not Noether symmetries, but which allow us…
On the k-Symplectic, k-Cosymplectic and Multisymplectic Formalisms of Classical Field Theories
Narciso Roman-Roy, Angel M. Rey, Modesto Salgado +1
The objective of this work is twofold: First, we analyze the relation between the k-cosymplectic and the k-symplectic Hamiltonian and Lagrangian formalisms in classical field theor…
Skinner-Rusk Unified Formalism for Optimal Control Systems and Applications
M. Barbero-Liñan, A. Echeverria-Enriquez, D. Martin de Diego +2
A geometric approach to time-dependent optimal control problems is proposed. This formulation is based on the Skinner and Rusk formalism for Lagrangian and Hamiltonian systems. The…
Some topics concerning the theory of singular dynamical systems
Narciso Roman-Roy
Some subjects related to the geometric theory of singular dynamical systems are reviewed in this paper. In particular, the following two matters are considered: the theory of canon…
k-cosymplectic classical field theories: Tulczyjew, Skinner--Rusk and Lie-algebroid formulations
Angel M. Rey, Narciso Roman-Roy, Modesto Salgado +1
The k-cosymplectic Lagrangian and Hamiltonian formalisms of first-order field theories are reviewed and completed. In particular, they are stated for singular and almost-regular sy…
Pre-multisymplectic constraint algorithm for field theories
M. de Leon, J. Marin-Solano, J. C. Marrero +2
We present a geometric algorithm for obtaining consistent solutions to systems of partial differential equations, mainly arising from singular covariant first-order classical field…
Extended Hamiltonian systems in multisymplectic field theories
Arturo Echeverria-Enriquez, Manuel de Leon, Miguel C. Munoz-Lecanda +1
We consider Hamiltonian systems in first-order multisymplectic field theories. We review the properties of Hamiltonian systems in the so-called restricted multimomentum bundle, inc…
Lagrangian-Hamiltonian unified formalism for field theory
A. Echeverría-Enríquez, C. López, J. Marín-Solano +2
The Rusk-Skinner formalism was developed in order to give a geometrical unified formalism for describing mechanical systems. It incorporates all the characteristics of Lagrangian a…
Geometric reduction in optimal control theory with symmetries
A. Echeverría-Enríquez, J. Marín-Solano, M. C. Muñoz-Lecanda +1
A general study of symmetries in optimal control theory is given, starting from the presymplectic description of this kind of system. Then, Noether's theorem, as well as the corres…
A geometrical analysis of the field equations in field theory
A. Echeverría-Enríquez, M. C. Muñoz-Lecanda, N. Román-Roy
In this review paper we give a geometrical formulation of the field equations in the Lagrangian and Hamiltonian formalisms of classical field theories (of first order) in terms of…
Singular Lagrangian Systems on Jet Bundles
M. de León, J. Marín-Solano, J. C. Marrero +2
The jet bundle description of time-dependent mechanics is revisited. The constraint algorithm for singular Lagrangians is discussed and an exhaustive description of the constraint…
On the construction of K-operators in field theories as sections along Legendre maps
A. Echeverría-Enríquez, J. Marín-Solano, M. C. Muñoz-Lecanda +1
The ``time-evolution operator'' in mechanics is a powerful tool which can be geometrically defined as a vector field along the Legendre map. It has been extensively used by several…
Time-dependent Lagrangians invariant by a vector field
M. C. Muñoz-Lecanda, N. Román-Roy, F. J. Yániz-Fernández
We study the reduction of non-autonomous regular Lagrangian systems by symmetries, which are generated by vector fields associated with connections in the configuration bundle of t…
Geometry of multisymplectic Hamiltonian first-order field theories
A. Echeverrí a-Enrí quez, M. C. Muñoz-Lecanda, N. Román-Roy
In the jet bundle description of Field Theories (multisymplectic models, in particular), there are several choices for the multimomentum bundle where the covariant Hamiltonian form…
Reduction of Presymplectic Manifolds with Symmetry
A. Echeverrí a-Enrí quez, M. C. Muñoz-Lecanda, N. Román-Roy
Actions of Lie groups on presymplectic manifolds are analyzed, introducing the suitable comomentum and momentum maps. The subsequent theory of reduction of presymplectic dynamical…