B Intermediate Axis Theorem - Intuitive Explanation

AI Thread Summary
The discussion focuses on the Intermediate Axis Theorem, particularly the instability of rotation about the middle axis. It highlights that examining a surface of fixed energy reveals six equilibria in three pairs, with the middle axis exhibiting saddle points, leading to instability. The "flipping" phenomenon observed in simulations corresponds to movement near a heteroclinic cycle between these saddle points. The conversation references previous videos and a Veritasium post for additional context. Overall, the thread emphasizes the dynamics of rotational stability and energy conservation in relation to the theorem.
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A simulation/animation/explanation based on the inertial frame only:

The previous videos referenced there are here:

See also this post for context on the Veritasium video: https://mathoverflow.net/a/82020

Note to mods: The previous thread is not open anymore so I opened a new one. Feel free to merge them.
 
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Here one of the more abstract approaches based on energy/momentum conservation. Unfortunately not much explanation in the video, and just a short description:



Robert Ghrist said:
Why is rotation about the middle axis unstable? If you examine a surface of fixed energy and look at the dynamics, you get six equilibria in three pairs -- rotation about each axis CW and CCW. These equilibria are centers for the longest and shortest axes. But for the middle axis -- the equilibria are saddles! The "flipping" seen in the previous video corresponds to traveling close to a heteroclinic cycle between saddle points.
 
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