54 citations · 305 across the 13 of their papers we have counts for
13 papers
Unified formalism for non-autonomous mechanical systems
María Barbero-Liñán, Arturo Echeverrí a-Enríquez, David Martín de Diego +2
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…
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…
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…
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…
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…
Multivector Field Formulation of Hamiltonian Field Theories: Equations and Symmetries
A. Echeverría-Enríquez, M. C. Muñoz-Lecanda, N. Román-Roy
We state the intrinsic form of the Hamiltonian equations of first-order Classical Field theories in three equivalent geometrical ways: using multivector fields, jet fields and conn…
Mathematical Foundations of Geometric Quantization
A. Echeverria-Enriquez, M. C. Munoz-Lecanda, N. Roman-Roy +1
In this review the foundations of Geometric Quantization are explained and discussed. In particular, we want to clarify the mathematical aspects related to the geometrical structur…
On the Multimomentum Bundles and the Legendre Maps in Field Theories
A. Echeverria-Enriquez, M. C. Munoz-Lecanda, N. Roman-Roy
We study the geometrical background of the Hamiltonian formalism of first-order Classical Field Theories. In particular, different proposals of multimomentum bundles existing in th…
Multivector Fields and Connections. Setting Lagrangian Equations in Field Theories
A. Echeverria-Enriquez, M. C. Munoz-Lecanda, N. Roman-Roy
The integrability of multivector fields in a differentiable manifold is studied. Then, given a jet bundle , it is shown that integrable multivector fields in ar…
Non-standard connections in classical mechanics
A. Echeverría-Enríquez, M. C. Muñoz-Lecanda, N. Román-Roy
In the jet-bundle description of first-order classical field theories there are some elements, such as the lagrangian energy and the construction of the hamiltonian formalism, whic…