Integrability of the $n$-dimensional axially symmetric Chaplygin sphere
Exactly Solvable and Integrable Systems
2019-11-21 v3 Mathematical Physics
math.MP
Abstract
We consider the -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 we perform the reduction by the associated symmetry and show that the reduced system is integrable by the Euler-Jacobi theorem.
Keywords
Cite
@article{arxiv.1906.00261,
title = {Integrability of the $n$-dimensional axially symmetric Chaplygin sphere},
author = {Luis C. Garcia-Naranjo},
journal= {arXiv preprint arXiv:1906.00261},
year = {2019}
}
Comments
15 pages. The third version includes minor corrections suggested by the referees of the journal "Regular and Chaotic Dynamics". The paper will be published in the special issue of RCD dedicated to S. A. Chaplygin (vol. 24, issue 5, 2019)