37 citations · 214 across the 15 of their papers we have counts for
9 papers · 1 filter
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…
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…
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…
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…