Luis C. García-Naranjo
Apdo Postal 20-726, Mexico City, 01000, Mexico
Bravo-Doddoli A., García-Naranjo L.
The Dynamics of an Articulated $n$-trailer Vehicle
2015, vol. 20, no. 5, pp. 497-517
We derive the reduced equations of motion for an articulated $n$-trailer vehicle that moves under its own inertia on the plane. We show that the energy level surfaces in the reduced space are $(n + 1)$-tori and we classify the equilibria within them, determining their stability. A thorough description of the dynamics is given in the case $n = 1$.
García-Naranjo L., Marrero J. C.
Non-Existence of an Invariant Measure for a Homogeneous Ellipsoid Rolling on the Plane
2013, vol. 18, no. 4, pp. 372-379
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 an invariant measure does not exist in the case when all of the semi-axes of the ellipsoid have different length.
Reduction of Almost Poisson Brackets for Nonholonomic Systems on Lie Groups
2007, vol. 12, no. 4, pp. 365-388
We present a systematic geometric construction of reduced almost Poisson brackets for nonholonomic systems on Lie groups with invariant kinetic energy metric and constraints. Our construction is of geometric interest in itself and is useful in the Hamiltonization of some classical examples of nonholonomic mechanical systems.