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2013
Impact Factor

# Luis García-Naranjo

Apdo Postal 20-726, Mexico City, 01000, Mexico
IIMAS-UNAM

## Publications:

 García-Naranjo L. C. Integrability of the $n$-dimensional Axially Symmetric Chaplygin Sphere 2019, vol. 24, no. 5, pp.  450-463 Abstract 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 DOI:10.1134/S1560354719050022
 Bravo-Doddoli A., García-Naranjo L. C. The Dynamics of an Articulated $n$-trailer Vehicle 2015, vol. 20, no. 5, pp.  497-517 Abstract 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 DOI:10.1134/S1560354715050019
 García-Naranjo L. C., 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 Abstract 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 DOI:10.1134/S1560354713040047
 García-Naranjo L. C. Reduction of Almost Poisson Brackets for Nonholonomic Systems on Lie Groups 2007, vol. 12, no. 4, pp.  365-388 Abstract 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 DOI:10.1134/S1560354707040028