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This article is cited in 2 scientific papers (total in 2 papers)
Sergey Chaplygin Memorial Issue
Integrability of the $n$-dimensional Axially Symmetric Chaplygin Sphere
Luis C. García-Naranjo Departamento de Matemáticas y Mecánica, IIMAS-UNAM,
Apdo. Postal 20-126, Col. San Ángel, Mexico City, 01000, Mexico
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.
Received: 05.06.2019 Accepted: 29.08.2019
Citation:
Luis C. García-Naranjo, “Integrability of the $n$-dimensional Axially Symmetric Chaplygin Sphere”, Regul. Chaotic Dyn., 24:5 (2019), 450–463
Linking options:
https://www.mathnet.ru/eng/rcd1021 https://www.mathnet.ru/eng/rcd/v24/i5/p450
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Abstract page: | 142 | References: | 27 |
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