Integrability of the $n$-dimensional Axially Symmetric Chaplygin Sphere

    2019, Volume 24, Number 5, pp.  450-463

    Author(s): 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, Volume 24, Number 5, pp. 450-463

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