Abstract—

The article considers the motion problem of three connected bodies in a homogeneous gravitational field (the generalized motion problem of a gyroscope in a gimbal). All stationary motions of the system, conditions of their stability and branching are found. Based on the analysis performed, it is shown that the complete atlas of Smale bifurcation diagrams for this problem consists of 24 maps that differ in the form of these diagrams. The paper presents one of the most complex Smale diagrams and describes how all the others are obtained from it.

中文翻译：

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三联体系统动力学的分叉Smale图

摘要-

本文考虑了均匀重力场中三个连接物体的运动问题（万向节中陀螺仪的广义运动问题）。找到系统的所有静止运动，其稳定性和分支的条件。根据执行的分析，表明针对此问题的完整的Smale分叉图集由24个图组成，这些图在这些图的形式上有所不同。本文介绍了最复杂的Smale图之一，并描述了如何从中获得其他所有图。