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.

中文翻译：

---

n维轴对称Chaplygin球的可积性

我们在假设n维Chaplygin球的质量分布是轴对称的前提下对其进行考虑。我们证明，对于围绕接触点的角动量为垂直的初始条件，动力学是准周期的。对于n = 4，我们通过相关的SO（3）对称性执行约简，并表明约简系统可通过Euler-Jacobi定理可积分。