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When a free-floating rigid body is rotating, the instantaneous rotation axis moves in a periodic manner on the intersection between the Angular momentum sphere and the Energy ellipsoid. (In the case of an instantaneous rotation around a main axis of inertia, this intersection is a point, and thus omega stays constant). This is known as the polhode (https://einstein.stanford.edu/highlights/hl_polhode_story.html).

Is it possible to compute the period of the polhode for any given 3D rigid body?

Thanks.

Maltergate
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  • To my knowledge the best resource for this issue: article, published in 2019, author: Nicholas Mecholsky, title: Analytic formula for the geometric phase of an Asymmetric top – Cleonis Jul 01 '22 at 08:14
  • The Gravity Probe B article contains a widespread misconception. While it is the case that an object with three different axes of inertia will exhibit a more complicated motion pattern: it is a stable pattern in the sense that the motion pattern is periodic. (Unstable and periodic are properties that cannot coexist) Nicholas Mecholsky demonstrates that periodicity. (Of course, in the real world there is always a non-zero dissipation of kinetic energy. In the real world this dissiplation is what prevents the polhode motion from being mathematically periodic.) – Cleonis Jul 01 '22 at 08:41
  • Thank you very much @Cleonis, after a speed reading of the article it seems that's what I'm looking for. Please turn your comment in answer so that I can validate it :) – Maltergate Jul 03 '22 at 22:12
  • Stackexchange has a policy (that I endorse) of discouraging link only answers. To qualify as an answer the submitter should at minimum present the relevant information in the linked resource, with the resource as general reference. You can, however, show your support with an upvote for the answer in which I discuss gyroscopic precession Inceidentally, I also recommend the two Dzhanibekov effect videos on the youtube channel Physics Unsimplified – Cleonis Jul 04 '22 at 16:31

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