16 citations · 96 across the 12 of their papers we have counts for
13 papers
The Spencer cohomology and integrability of multisymplectic structures
Manuel de León, Rubén Izquierdo-López, Manuel Lainz
We study the integrability problem of multisymplectic structures, by identifying them as -structures. Applying the theory of Spencer cohomology, we give conditions on a multisym…
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…
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…
The Herglotz variational principle for dissipative field theories
Jordi Gaset, Manuel Lainz, Arnau Mas +1
In the recent years, with the incorporation of contact geometry, there has been a renewed interest in the study of dissipative or non-conservative systems in physics and other area…
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…
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…
The Herglotz principle and vakonomic dynamics
Manuel de León, Manuel Lainz, Miguel C. Muñoz-Lecanda
In this paper we study vakonomic dynamics on contact systems with nonlinear constraints. In order to obtain the dynamics, we consider a space of admisible paths, which are the ones…
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…
A review on contact Hamiltonian and Lagrangian systems
Manuel de León, Manuel Lainz
Contact Hamiltonian dynamics is a subject that has still a short history, but with relevant applications in many areas: thermodynamics, cosmology, control theory, and neurogeometry…
Optimal control, contact dynamics and Herglotz variational problem
Manuel de León, Manuel Lainz, Miguel C. Muñoz-Lecanda
In this paper we combine two main topics in mechanics and optimal control theory: contact Hamiltonian systems and Pontryagin Maximum Principle. As an important result, among others…
Plasma in monopole background is not twisted Poisson
Manuel Lainz, Cristina Sardon, Alan Weinstein
For a particle in the magnetic field of a cloud of monopoles, the naturally associated 2-form on phase space is not closed, and so the corresponding bracket operation on functions…