We solved the Poisson equations, obtaining their exact solution in elementary functions for the rotation matrix of a free asymmetrical body with angular velocity vector lying on separatrices. This allows us to discuss the temporal evolution of Dzhanibekov’s nut directly in the laboratory system, where it is observed. The rotation matrix depends on two parameters with clear physical interpretation as a frequency and a damping factor of the solution. Qualitative analysis of the solution shows that it properly describes a single-jump Dzhanibekov effect.

中文翻译：

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不对称体：初等函数和 Dzhanibekov 效应中旋转矩阵的解析解示例


我们求解了泊松方程，获得了角速度矢量位于分网上的自由非对称体旋转矩阵初等函数中的精确解。这使我们能够直接在实验室系统中观察贾尼别科夫坚果的时间演变。旋转矩阵取决于两个具有明确物理解释的参数，即解的频率和阻尼因子。对解的定性分析表明，它正确地描述了单跳 Dzhanibekov 效应。