新年还没开过新帖，我发一帖。之前的kovalevsky top太难了，今天来看最简单的陀螺——欧拉陀螺。其实就是绕定点的刚体转动。
本帖主题：刚体稳定性定理
先看视频，https://www.bilibili.com/video/BV1Gi4y157Rn/
定理：刚体围绕本身的3个惯量主轴旋转，不妨设I1>I2>I3,那么绕长轴和短轴的旋转是稳定的，绕中等长度轴的旋转是不稳定的。
https://en.wikipedia.org/wiki/Tennis_racket_theorem

It is also dubbed the Dzhanibekov effect, after Soviet cosmonaut Vladimir Dzhanibekov who noticed one of the theorem's logical consequences while in space in 1985[1] although the effect was already known for at least 150 years before that.

Louis Poinsot, Théorie nouvelle de la rotation des corps, Paris, Bachelier, 1834, 170 p. OCLC 457954839 : historically, the first mathematical description of this effect.

其实中学时代扔书扔了不知多少次了，但是当第一次看见这个定理的时候，还是感到无法接受，然后自己又默默的扔了无数回。

虽然只是是刚体，里面的力学内涵还是丰富到出乎了想象。刚体稳定性虽说不是特别简单，但也不难。具体推导在Marsden的那本Introduction to mechanics and symmetry里面最后一章。证明要点其实是附件这张图


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修改:vinbo FROM 45.89.228.*
FROM 202.121.181.*