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 SO(3) symmetry and show that
the reduced system is integrable by the Euler – Jacobi theorem.
\Bibitem{Gar19}
\by Luis C. Garc{\'\i}a-Naranjo
\paper Integrability of the $n$-dimensional Axially Symmetric Chaplygin Sphere
\jour Regul. Chaotic Dyn.
\yr 2019
\vol 24
\issue 5
\pages 450--463
\mathnet{http://mi.mathnet.ru/rcd1021}
\crossref{https://doi.org/10.1134/S1560354719050022}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4015391}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85073260469}
Linking options:
https://www.mathnet.ru/eng/rcd1021
https://www.mathnet.ru/eng/rcd/v24/i5/p450
This publication is cited in the following 2 articles:
Vladimir Dragović, Borislav Gajić, Bozidar Jovanović, “Spherical and Planar Ball Bearings — a Study of Integrable Cases”, Regul. Chaotic Dyn., 28:1 (2023), 62–77
V. Dragovic, B. Gajic, B. Jovanovic, “Demchenko's nonholonomic case of a gyroscopic ball rolling without sliding over a sphere after his 1923 belgrade doctoral thesis”, Theor. Appl. Mech., 47:2 (2020), 257–287
Citation in format AMSBIB
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