Luis García-Naranjo

Luis García-Naranjo
Via VIII Febbraio 2, 35122 Padova, Italy
University of Padova


García-Naranjo L. C.
We consider the $n$-dimensional Chaplygin sphere under the assumption that the mass distribution of the sphere is axisymmetric. We prove that, for initial conditions whose angular momentum about the contact point is vertical, the dynamics is quasi-periodic. For $n=4$ we perform the reduction by the associated $\mathrm{SO}(3)$ symmetry and show that the reduced system is integrable by the Euler–Jacobi theorem.
Keywords: non-holonomic dynamics, integrability, quasi-periodicity, symmetry, singular reduction
Citation: García-Naranjo L. C.,  Integrability of the $n$-dimensional Axially Symmetric Chaplygin Sphere, Regular and Chaotic Dynamics, 2019, vol. 24, no. 5, pp. 450-463
Bravo-Doddoli A., García-Naranjo L. C.
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 $n = 1$.
Keywords: dynamics, nonholonomic constraints, $n$-trailer vehicle
Citation: Bravo-Doddoli A., García-Naranjo L. C.,  The Dynamics of an Articulated $n$-trailer Vehicle, Regular and Chaotic Dynamics, 2015, vol. 20, no. 5, pp. 497-517
García-Naranjo L. C., Marrero J. C.
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.
Keywords: nonholonomic mechanical systems, invariant volume forms, symmetries, reduction
Citation: García-Naranjo L. C., Marrero J. C.,  Non-Existence of an Invariant Measure for a Homogeneous Ellipsoid Rolling on the Plane, Regular and Chaotic Dynamics, 2013, vol. 18, no. 4, pp. 372-379
García-Naranjo L. C.
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.
Keywords: nonholonomic systems, almost Poisson brackets, hamiltonization, geometric reduction
Citation: García-Naranjo L. C.,  Reduction of Almost Poisson Brackets for Nonholonomic Systems on Lie Groups, Regular and Chaotic Dynamics, 2007, vol. 12, no. 4, pp. 365-388

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