77 citations · 818 across the 61 of their papers we have counts for
45 papers · 1 filter
Higher-order and non-geometric symmetries and Noether's theorem in k-cosymplectic Hamiltonian field theory
Manuel de León, Xuefeng Zhao
In this paper, we investigate higher-order symmetries and non-geometric symmetries within the framework of -cosymplectic Hamiltonian field theory. We introduce the concept of ge…
A new perspective on nonholonomic brackets and Hamilton-Jacobi theory
Manuel de León, Manuel Lainz, Asier López-Gordón +1
The nonholonomic dynamics can be described by the so-called nonholonomic bracket on the constrained submanifold, which is a non-integrable modification of the Poisson bracket of th…
Jacobi structure for dissipative mechanical systems on Lie Algebroids
Alexandre Anahory Simoes, Leonardo Colombo, Manuel de Leon +2
We extend the Jacobi structure from and to and , respectively, where is a Lie alge…
Nonholonomic brackets: Eden revisited
Manuel de León, Manuel Lainz, Asier López-Gordón +1
The nonholonomic dynamics can be described by the so-called nonholonomic bracket in the constrained submanifold, which is a non-integrable modification of the Poisson bracket of th…
Hamilton-Jacobi theory for nonholonomic and forced hybrid mechanical systems
Leonardo Colombo, Manuel de León, María Emma Eyrea Irazú +1
A hybrid system is a system whose dynamics is given by a mixture of both continuous and discrete transitions. In particular, these systems can be utilised to describe the dynamics…
Hamilton-Jacobi theory and integrability for autonomous and non-autonomous contact systems
Manuel de León, Manuel Lainz, Asier López-Gordón +1
In this paper, we study the integrability of contact Hamiltonian systems, both time-dependent and independent. In order to do so, we construct a Hamilton--Jacobi theory for these s…
A geometric model for non-uniform processes of morphogenesis
V. M. Jiménez, M. de León
In this paper we present an application of the groupoid theory to the study of relevant case of material evolution phenomena, the \textit{process of morphogenesis}. Our theory is i…
Contact Lagrangian systems subject to impulsive constraints
Leonardo J. Colombo, Manuel de León, Asier López-Gordón
We describe geometrically contact Lagrangian systems under impulsive forces and constraints, as well as instantaneous nonholonomic constraints which are not uniform along the confi…
Discrete Hamilton-Jacobi theory for systems with external forces
Manuel de León, Manuel Lainz, Asier López-Gordón
This paper is devoted to discrete mechanical systems subject to external forces. We introduce a discrete version of systems with Rayleigh-type forces, obtain the equations of motio…
Geometric Hamilton-Jacobi theory for systems with external forces
Manuel de León, Manuel Lainz, Asier López-Gordón
In this paper, we develop a Hamilton-Jacobi theory for forced Hamiltonian and Lagrangian systems. We study the complete solutions, particularize for Rayleigh systems and present so…
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, constants of the motion and reduction of mechanical systems with external forces
Manuel de León, Manuel Lainz, Asier López-Gordón
This paper is devoted to the study of mechanical systems subjected to external forces in the framework of symplectic geometry. We obtain a Noether's theorem for Lagrangian systems…
On the geometry of discrete contact mechanics
Alexandre Anahory Simoes, David Martín de Diego, Manuel de León +1
In this paper, we continue the construction of variational integrators adapted to contact geometry started in \cite{VBS}, in particular, we introduce a discrete Herglotz Principle…
Cauchy data space and multisymplectic formulation of conformal classical field theories
Ogul Esen, Manuel de León, Cristina Sardón +1
In this article we inspect the dynamics of classical field theories with a local conformal behavior. Our interest in the multisymplectic setting comes from its suitable description…
Hamilton-Jacobi Formalism on Locally Conformally Symplectic Manifolds
Oğul Esen, Manuel de León, Cristina Sardón +1
In this article we provide a Hamilton-Jacobi formalism in locally conformally symplectic manifolds. Our interest in the Hamilton-Jacobi theory comes from the suitability of this th…
Characteristic distribution: An application to material bodies
V. M. Jiménez, M. de León, M. Epstein
Associated to each material body there exists a groupoid consisting of all the material isomorphisms connecting the points of $\mathcal{…
A Hamilton-Jacobi theory for implicit differential systems
O. Esen, M. de León, C. Sardón
In this paper, we propose a geometric Hamilton-Jacobi theory for systems of implicit differential equations. In particular, we are interested in implicit Hamiltonian systems, descr…
A geometric Hamilton--Jacobi theory on a Nambu-Jacobi manifold
M. de León, C. Sardón
In this paper we propose a geometric Hamilton--Jacobi theory on a Nambu--Jacobi manifold. The advantange of a geometric Hamilton--Jacobi theory is that if a Hamiltonian vector fiel…
Geometry of the discrete Hamilton--Jacobi equation. Applications in optimal control
M. de León, C. Sardón
In this paper, we review the discrete Hamilton--Jacobi theory from a geometric point of view. In the discrete realm, the usual geometric interpretation of the Hamilton--Jacobi theo…
Cosymplectic and contact structures to resolve time-dependent and dissipative hamiltonian systems
M. de León, C. Sardón
In this paper, we apply the geometric Hamilton--Jacobi theory to obtain solutions of classical hamiltonian systems that are either compatible with a cosymplectic or a contact struc…
On the Geometry of the Hamilton-Jacobi Equation and Generating Functions
Sebastián Ferraro, Manuel de León, Juan Carlos Marrero +2
In this paper we develop a geometric version of the Hamilton-Jacobi equation in the Poisson setting. Specifically, we "geometrize" what is usually called a complete solution of the…
A geometric Hamilton--Jacobi theory for a Nambu--Poisson structure
M. de Leon, C. Sardon
The Hamilton-Jacobi theory is a formulation of Classical Mechanics equivalent to other formulations as Newton's equations, Lagrangian or Hamiltonian Mechanics. It is particulary us…
Hamilton-Jacobi theory, Symmetries and Coisotropic Reduction
Manuel de León, David Martín de Diego, Miguel Vaquero
Reduction theory has played a major role in the study of Hamiltonian systems. On the other hand, the Hamilton-Jacobi theory is one of the main tools to integrate the dynamics of ce…
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…