Ellipsoids and The Bizarre Behaviour of Rotating Bodies

From Standup Mathematician.

Derek’s video: The Bizarre Behavior of Rotating Bodies, Explained
https://www.youtube.com/watch?v=1VPfZ_XzisU

Based on this amazing footage: Dancing T-handle in zero-g
https://www.youtube.com/watch?v=1n-HMSCDYtM

Terence Tao’s original answer, with update.
https://mathoverflow.net/questions/81960/the-dzhanibekov-effect-an-exercise-in-mechanics-or-fiction-explain-mathemat

Support me on Patreon and I can make more video like this!
https://www.patreon.com/standupmaths

We are sat so close because we filmed this in the “before times” of late 2019.

Huge thanks to Helen Czerski for spinning a book in zero-G for us.
https://www.youtube.com/watch?v=qKbHkYllIr0
https://cosmicshambles.com/video/webseries/zerog

Cosmic Shambles (who convinced ESA to launch Helen) also have a Patreon:
https://www.patreon.com/cosmicshambles

Ben Sparks made the ellipsoid animations for me. Check out their GeoGebra files here:
https://www.geogebra.org/m/kuntcc5a
https://www.geogebra.org/u/sparksmaths

Rotating 3D book was thanks to Tim Waskett of Stone Baked Games.
https://www.stonebakedgames.com/

There are plenty more Matt and Hugh videos to learn about moments of inertia and suchlike.
https://www.youtube.com/playlist?list=PLhtC92GarkjwweBkdrq5uPzEjnRF6ncCV

Hugh Hunt is the Cambridge University Reader in Engineering Dynamics and Vibration. I know!
http://www2.eng.cam.ac.uk/~hemh1/

Zero G footage courtesy The Cosmic Shambles Network working in association with the European Space Agency. In flight footage shot by Melanie Cowan. External plane footage courtesy Novespace.

CORRECTIONS
– At 11:00 and 14:23 I say the axes correspond to the axes of rotation but technically they represent the three different directions of spin. Which is why they are labelled with omegas representing the angular velocities in those directions.
– At 05:52 the ellipsoid equation should be “volume” not “area”. First pointed out by Ihsan Khairir. My fault for not paying attention editing the text after copying the previous equations.
– Oh my goodness. At 11:50 we missed an “L” in ellipsoid. First pointed out by Daniel Burger. I’m so embarrassed.
– Let me know if you spot any other mistakes. Or, you know, make a whole video about it.

As always: thanks to Jane Street who support my channel. They’re amazing.
https://www.janestreet.com/

Filming and editing by Trunkman Productions
Additional filming by Melanie Cowan
Audio by Peter Doggart
Music by Howard Carter
Design by Simon Wright and Adam Robinson

MATT PARKER: Stand-up Mathematician
Website: http://standupmaths.com/
US book: https://www.penguinrandomhouse.com/books/610964/humble-pi-by-matt-parker/
UK book: https://mathsgear.co.uk/products/5b9fa76f230ffa140094dc43
Nerdy maths toys: http://mathsgear.co.uk/