Bizarre behavior of rotating bodies explained
- REFERENCES: Prof. Terry Tao's Math Overflow Explanation: ve42.co/Tao
- The Twisting Tennis Racket: Ashbaugh, M.S., Chicone, C.C. & Cushman, R.H. J Dyn Diff Equat (1991) 3: 67. doi.org/10.1007/BF01049489
- Janibekov’s effect and the laws of mechanics: Petrov, A.G. & Volodin, S.E. Dokl. Phys. (2013) 58: 349. https://doi.org/10.1134/S102833581308...
- Tumbling Asteroids: Prave et al. https://doi.org/10.1016/j.icarus.2004...
- The Exact Computation of the Free Rigid Body Motion and Its Use in Splitting Methods: SIAM J. Sci. Comput., 30(4), 2084–2112: E. Celledoni, F. Fassò, N. Säfström, and A. Zanna: doi.org/10.1137/070704393
This is a further discussion by Henry Reich that helps summarize why Axes 1 and 3 are generally stable while Axis 2 is not:
In general, imagine that, because the object can rotate in a bunch of different directions, the components of energy and momentum could be free to change, while the total momentum stays constant.
- (This can easily be shown from conservation of energy and momentum equations. And this is also fairly intuitive from the fact that kinetic energy is proportional to velocity squared, while momentum is proportional to velocity. So in the case of Axis 1, the smaller masses will have to be spinning faster for a given momentum. They will thus have more energy, and vice versa for Axis 3, where all the masses are spinning: The energy will be lowest).