37 citations · 214 across the 15 of their papers we have counts for
15 papers
Affine generalizations of the nonholonomic problem of a convex body rolling without slipping on the plane
M. Costa Villegas, L. C. García-Naranjo
We introduce a class of examples which provide an affine generalization of the nonholonomic problem of a convex body rolling without slipping on the plane. We investigate dynamical…
Almost-Poisson brackets for nonholonomic systems with gyroscopic terms and Hamiltonisation
L. C. García-Naranjo, J. C. Marrero, D. Martín de Diego +1
We extend known constructions of almost-Poisson brackets and their gauge transformations to nonholonomic systems whose Lagrangian is not mechanical but possesses a gyroscopic term…
Integrability of the -dimensional axially symmetric Chaplygin sphere
Luis C. Garcia-Naranjo
We consider the -dimensional Chaplygin sphere under the assumption that the mass distribution of the sphere is axisymmetric. We prove that for initial conditions whose angular m…
Integrability and dynamics of the n-dimensional symmetric Veselova top
Francesco Fassò, Luis C. García-Naranjo, James Montaldi
We consider the the n-dimensional generalisation of the nonholonomic Veselova problem. We derive the reduced equations of motion in terms of the mass tensor of the body and determi…
Reduction and relative equilibria for the 2-body problem in spaces of constant curvature
A. V. Borisov, L. C. García-Naranjo, I. S. Mamaev +1
We consider the two-body problem on surfaces of constant non-zero curvature and classify the relative equilibria and their stability. On the hyperbolic plane, for each q>0 we show…
Gauge momenta as Casimir functions of nonholonomic systems
Luis C. Garcia-Naranjo, James Montaldi
We consider nonholonomic systems with symmetry possessing a certain type of first integrals that are linear in the velocities. We develop a systematic method for modifying the stan…
The geometric discretisation of the Suslov problem: a case study of consistency for nonholonomic integrators
Luis C. Garcia-Naranjo, Fernando Jimenez
Geometric integrators for nonholonomic systems were introduced by Cortés and Martínez in [Nonholonomic integrators, Nonlinearity, 14, 2001] by proposing a discrete Lagrange-D'Alemb…
The dynamics of an articulated -trailer vehicle
Alejandro Bravo-Doddoli, Luis C. García-Naranjo
We derive the reduced equations of motion for an articulated -trailer vehicle that moves under its own inertia on the plane. We show that the energy level surfaces in the reduce…
Poisson structures on smooth 4-manifolds
Luis C. García-Naranjo, Pablo Suárez-Serrato, Ramón Vera
We show that every closed oriented smooth 4-manifold admits a complete singular Poisson structure in each homotopy class of maps to the 2-sphere. The rank of this structure is 2 ou…
Non-existence of an invariant measure for a homogeneous ellipsoid rolling on the plane
Luis C. García-Naranjo, Juan C. Marrero
It is known that the reduced equations for an axially symmetric homogeneous ellipsoid that rolls without slipping on the plane possess a smooth invariant measure. We show that such…
Unimodularity and preservation of volumes in nonholonomic mechanics
Yuri N. Fedorov, Luis C. García-Naranjo, Juan C. Marrero
The equations of motion of a mechanical system subjected to nonholonomic linear constraints can be formulated in terms of a linear almost Poisson structure in a vector bundle. We s…
Gauge Transformations, Twisted Poisson Brackets and Hamiltonization of Nonholonomic Systems
Paula Balseiro, Luis García-Naranjo
In this paper we study the problem of Hamiltonization of nonholonomic systems from a geometric point of view. We use gauge transformations by 2-forms (in the sense of Severa and We…
The Hydrodynamic Chaplygin Sleigh
Yuri N. Fedorov, Luis C. Garcia-Naranjo
We consider the motion of rigid bodies in a potential fluid subject to certain nonholonomic constraints and show that it is described by Euler--Poincaré--Suslov equations. In the 2…
-Chaplygin systems with internal symmetries, truncation, and an (almost) symplectic view of Chaplygin's ball
Simon Hochgerner, Luis Garcia-Naranjo
Via compression ([11, 7]) we write the -dimensional Chaplygin sphere system as an almost Hamiltonian system on with internal symmetry group . We show how thi…
Reduction of Almost Poisson brackets and Hamiltonization of the Chaplygin Sphere
Luis C. Garcia-Naranjo
We construct different almost Poisson brackets for nonholonomic systems than those existing in the literature and study their reduction. Such brackets are built by considering non-…