Intermediate Axis Theorem - Intuitive Explanation

[A.T.]

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.

 

[A.T.]

Here one of the more abstract approaches based on energy/momentum conservation. Unfortunately not much explanation in the video, and just a short description:

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.