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2013
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# Luis García-Naranjo

Via VIII Febbraio 2, 35122 Padova, Italy
 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