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.
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Acknowledgements
I am grateful to the anonymous referees for remarks that helped me to improve this paper. I am very thankful to J. Montaldi for a conversation that inspired this research during my recent visit to the University of Manchester. I acknowledge support of the Alexander von Humboldt Foundation for a Georg Forster Experienced Researcher Fellowship that funded a research visit to TU Berlin where this work was done. Finally, I express my gratitude to A.V. Borisov for his invitation to submit a paper for the special issue of Regular and Chaotic Dynamics in honour of S.A. Chaplygin on the occasion of his 150th birthday.
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Dedicated to S.A. Chaplygin on the occasion of his 150th birthday
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The authors declare that they have no conflicts of interest.
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García-Naranjo, L.C. Integrability of the n-dimensional Axially Symmetric Chaplygin Sphere. Regul. Chaot. Dyn. 24, 450–463 (2019). https://doi.org/10.1134/S1560354719050022
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DOI: https://doi.org/10.1134/S1560354719050022