# Asier López-GordónInstituto de Ciencias Matemáticas (ICMAT) · Geometric Mechanics and Control Research Group

Asier López-Gordón

Master of Science

Predoctoral researcher

## About

18

Publications

1,059

Reads

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36

Citations

Citations since 2017

Introduction

I am mainly interested in geometric mechanics and mathematical physics. More specifically, I am carrying out a PhD thesis on the geometry of dissipative processes.

Education

September 2021 - August 2025

September 2020 - June 2021

September 2016 - July 2020

## Publications

Publications (18)

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 with external forces, among other results regarding symmetries and conserved quantities. We particularize our results for the so-called Rayleigh dissipation, i.e., extern...

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 motion and characterize the equivalence for these systems. Additionally, we obtain a Noether’s theorem and other theorem characterizing the Lie subalgebra of symmetries of a f...

This paper discusses reduction by symmetries for autonomous and non-autonomous forced mechanical systems with inelastic collisions. In particular, we introduce the notion of generalized hybrid momentum map and hybrid constants of the motion to give general conditions on whether it is possible to perform symmetry reduction for Hamiltonian and Lagran...

In this paper we obtain two Hamilton-Jacobi equations for time dependent contact Hamiltonian systems. In these systems there is a dissipation parameter and the fact of obtaining two equations reflects whether we are looking for solutions that depend on this parameter or not. We also study the existence of complete solutions and the integrability pr...

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 some examples. Additionally, we present a method for the reduction and reconstruction of the Hamilton-Jacobi problem for forced Hamiltonian systems with symmetry. Furthermo...

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 the ambient space, in this case, of the canonical bracket in the cotangent bundle of the configuration manifold. This bracket was defined by Cantrijn et al. and Ibort et al...

Integrability of Hamiltonian systems is often identified with complete integrability, or Liouville integrability, that is, the existence of as many independent integrals of motion in involution as the dimension of the phase space. Under certain regularity conditions, Liouville--Arnold theorem states that the invariant geometric structure associated...

In contact Hamiltonian systems, the so-called dissipated quantities are akin to conserved quantities in classical Hamiltonian systems. In this paper, we prove a Noether's theorem for non-autonomous contact Hamiltonian systems, characterizing a class of symmetries which are in bijection with dissipated quantities. We also study other classes of symm...

A hybrid system is a system whose dynamics are controlled by a mixture of both continuous and discrete transitions. The geometric framework for the Hamilton-Jacobi theory is developed to study this theory for hybrid dynamical systems, in particular, forced and nonholonomic hybrid systems. We state the corresponding Hamilton-Jacobi equations for the...

We describe geometrically contact Lagrangian systems under impulsive forces and constraints, as well as instantaneous nonholonomic constraints which are not uniform along the configuration space. In both situations, the vector field describing the dynamics of a contact Lagrangian system is determined by defining projectors to evaluate the constrain...

Forced variational integrators are given by the discretization of the Lagrange-d'Alembert principle for systems subject to external forces, and have proved useful for numerical simulation studies of complex dynamical systems. In this paper we model a passive walker with foot slip by using techniques of geometric mechanics, and we construct forced v...

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. In particular, we develop a Herglotz variational principle for non-smooth action-dependent Lagrangians which leads to the preservation of energy and momentum at impacts...

We describe geometrically contact Lagrangian systems under impulsive forces and constraints, as well as instantaneous nonholonomic constraints which are not uniform along the configuration space. In both situations, the vector field describing the dynamics of a contact Lagrangian system is determined by defining projectors to evaluate the constrain...

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 hybrid Lagrangian system subject to non-conservative external forces, emphasizing the case of cyclic coordinates. We illustrate the applicability of the symmetry reduction...

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 motion and characterize the equivalence for these systems. Additionally, we obtain a Noether's theorem and other theorem characterizing the Lie subalgebra of symmetries of a f...

Geometric mechanics is a branch of mathematical physics that studies classical mechanics of particles and fields from the point of view of geometry. In a geometric language, symmetries can be expressed in a natural manner as vector fields that generate the corresponding symmetry group. Moreover, with the geometric machinery, the phase space of a me...

We analyse the exact expression and asymptotic behaviour of the entanglement entropy of some integrable spin chains. Our calculations are explicitly carried out for the XX chain, although most of them will be generalizable to other free fermion or equivalent systems. We start by introducing the von Neumann entanglement entropy as a measure of the d...

## Projects

Project (1)

Mechanical systems with external forces are usual in physics and engineering, but they can also arise after a process of reduction of a nonholonomic system with symmetries. We have obtained several results for these systems, regarding symmetries, constants of the motion, reduction, Hamilton-Jacobi theory and discretization, generalizing well-known results from Hamiltonian and Lagrangian mechanics in the framework of symplectic geometry.