77 citations · 818 across the 61 of their papers we have counts for
64 papers
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…
The nonholonomic bracket on contact mechanical systems
Manuel De León, Víctor M. Jiménez
In this paper we study contact nonholonomic mechanical sys\-tems. We construct a general framework for non-holonomic constraints in contact geometry and, in this framework, we defi…
On Non-autonomous Hamiltonian Dynamics, Dual Spaces, and Kinetic Lifts
Begüm Ateşli, Oğul Esen, Manuel de León +1
Vlasov kinetic theory is the dynamics of a bunch of particles flowing according to symplectic Hamiltonian dynamics. More recently, this geometry has been extended to contact Hamilt…
Contact formalism for dissipative mechanical systems on Lie algebroids
Alexandre Anahory Simoes, Leonardo Colombo, Manuel de Leon +2
In this paper, we introduce a geometric description of contact Lagrangian and Hamiltonian systems on Lie algebroids in the framework of contact geometry, using the theory of prolon…
A review on coisotropic reduction in Symplectic, Cosymplectic, Contact and Co-contact Hamiltonian systems
Manuel de León, Rubén Izquierdo-López
In this paper we study the coisotropic reduction in different types of dynamics according to the geometry of the corresponding phase space. The relevance of the coisotropic reducti…
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…
New notions of uniformity and homogeneity of Cosserat media
V. M. Jiménez, M. De León
In this paper, we study internal properties of a Cosserat media. In fact, by using groupoids and smooth distributions, we obtain a three canonical equations. The \textit{non-holono…
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…
Liouville-Arnold theorem for homogeneous symplectic and contact Hamiltonian systems
Leonardo Colombo, Manuel de León, Manuel Lainz +1
A Hamiltonian system is completely integrable (in the sense of Liouville) if there exist as many independent integrals of motion in involution as the dimension of the configuration…
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…
Nonsmooth Herglotz variational principle
Asier López-Gordón, Leonardo Colombo, Manuel de León
In this paper, the theory of smooth action-dependent Lagrangian mechanics (also known as contact Lagrangians) is extended to a non-smooth context appropriate for collision problems…
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…
On Locally Conformally Cosymplectic Hamiltonian Dynamics and Hamilton-Jacobi Theory
Begüm Ateşli, Oğul Esen, Manuel de León +1
Cosymplectic geometry has been proven to be a very useful geometric background to describe time-dependent Hamiltonian dynamics. In this work, we address the globalization problem o…
Reviewing the Geometric Hamilton-Jacobi Theory concerning Jacobi and Leibniz identities
O. Esen, M. de León, M. Lainz +2
In this survey, we review the classical Hamilton Jacobi theory from a geometric point of view in different geometric backgrounds. We propose a Hamilton Jacobi equation for differen…
Hybrid Routhian reduction for simple hybrid forced Lagrangian systems
María Emma Eyrea Irazú, Asier López-Gordón, Leonardo J. Colombo +1
This paper discusses Routh reduction for simple hybrid forced mechanical systems. We give general conditions on whether it is possible to perform symmetry reduction for a simple hy…
Generalized hybrid momentum maps and reduction by symmetries of forced mechanical systems with inelastic collisions
Leonardo J. Colombo, Manuel de León, María Emma Eyrea Irazú +1
This paper discusses reduction by symmetries for autonomous and non-autonomous forced mechanical systems with inelastic collisions. In particular, we introduce the notion of genera…
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…