Gyros & Tops in space

[Iacopo]

I do have a quip about the animation. It shows the little masses continuing to rotate in the same direction with respect to the large masses for the second period. I believe they should reverse direction, and the direction should oscillate back and forth (in this relative frame of motion). The way I think about it, if m1 starts a little above the y axis, it will finish a little above the (-)y axis on the other side, not at 180 degrees.

A difficult question.

In Tao's explanation, the force (and therefore acceleration) on the small mass is proportional to it's distance to the y axis. It's accelerated until it reaches the z axis and decelerated after that. So it should have zero speed when it reaches it's initial high over the y axis on the other side. From there it should reverse directions. Like a ball oscillating in the valley between two peaks.

Sorry, Ta0, I didn't understand. You mean at 9:24, when the plate continues tilting in the same direction instead of tilting back.
I believe you are right, it seems like an inaccuracy in the animation.

[Jeremy McCreary]

Just out on Veritasium -- a (kind of) intuitive explanation of the T-handle's flipping behavior...

https://youtu.be/1VPfZ_XzisU

The famous mathematician who came up with this so-called "intuitive" explanation of the flipping behavior of triaxial bodies (like tennis rackets, T-handles, and wing nuts) has since revised it -- and complicated it a good bit in the process.

Which prompted this purportedly "more intuitive" explanation based on the 3D intersection of a triaxial body's energy and momental ellipsoids...

https://youtu.be/l51LcwHOW7s

This one explains how a triaxial body can flip while conserving, as it must, both its kinetic energy and the magnitude (though generally not the direction) of its angular momentum vector. (More on how these necessities actually constrain the body's observed motion here.)

Problem is, this 2nd "explanation" doesn't explain why T-handles and wing nuts in space routinely take this opportunity to flip, and to routinely keep flipping back and forth at seemingly regular intervals. Hopefully that strength of the original explanation survived the revision (which I have not read).

[ta0]

Another demonstration in space for the intermediate axis theorem by Sultan AlNeyadi:

https://twitter.com/Astro_Alneyadi/stat ... 4031537226