The problem of rolling a nonholonomic bundle of two bodies is considered: a spherical shell with a rigid body rotating along the axis of symmetry, on which rotors spinning relative to this body are fastened. This problem can be regarded as a distant generalization of the Chaplygin ball problem. The reduced system is studied by analyzing Poincaré maps constructed in Andoyer – Deprit variables. A classification of Poincaré maps of the reduced system is carried out, the behavior of the contact point is studied, and the cases of chaotic oscillations of the system are examined in detail. To study the nature of the system’s chaotic behavior, a map of dynamical regimes is constructed. The Feigenbaum type of attractor is shown.

中文翻译：

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两个非完整混沌系统。第二部分 关于两个实体的非完整捆绑的滚动

考虑了两个物体的非完整束的滚动问题：具有沿对称轴旋转的刚体的球形壳体，相对于该物体旋转的转子固定在该球形壳体上。这个问题可以看作是Chaplygin球问题的遥远概括。通过分析在Andoyer-Deprit变量中构造的庞加莱图来研究简化系统。对简化系统的庞加莱图进行了分类，研究了接触点的行为，并详细研究了系统的混沌振动情况。为了研究系统混沌行为的性质，构建了动态状态图。显示了费根鲍姆吸引子类型。