The motion of a spherical robot with periodically changing moments of inertia, internal rotors and a displaced center of mass is considered. It is shown that, under some restrictions on the displacement of the center of mass, the system of interest features chaotic dynamics due to separatrix splitting. A stability analysis is made of the upper equilibrium point of the ball and of the periodic solution arising in its neighborhood, in the case of periodic rotation of the rotors. It is shown that the lower equilibrium point can become unstable in the case of fixed rotors and periodically changing moments of inertia.

中文翻译：

---

具有可变惯性矩和重心位移的球形机器人的动力学

考虑具有周期性变化的惯性矩，内部转子和位移的质心的球形机器人的运动。结果表明，在对质心位移有一定限制的情况下，感兴趣的系统具有由于分离线分裂而引起的混沌动力学。在转子周期性旋转的情况下，对球的上平衡点和在其附近产生的周期解进行了稳定性分析。结果表明，在转子固定且惯性矩周期性变化的情况下，下平衡点可能变得不稳定。