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[Jeremy McCreary]

Yes or no: Is it valid to call the rotation about the vertical here "precession"?

Of course! Isn't that the classic example of (torque induced) precession?

Yes. Richard Feynman, in explaining a dynamically equivalent gyroscope experiment, famously said,

You have to go down a little to go round.

He also showed that the inner gimbal quickly reaches and holds an equilibrium tilt as steady precession proceeds, despite the ongoing gravitational torque applied to it by the weight still hanging from it. No further acceleration of inner gimbal tilt required to maintain precession.

This is exactly what's going on in the LEGO demo. Only the steady torque on the inner gimbal in this case is supplied by a stepper motor visible near one of the lower corners of the outer gimbal.

This stepper motor turns exactly 90° at full voltage. The bang-bang remote control used has only 3 states -- zero voltage, full forward, and full reverse.

Yet the inner gimbal reaches and holds the same equilibrium tilt each time the remote is held on. And this tilt is a good bit less than 90°.  There are no hard stops to keep the inner gimbal from tilting more.

Hence, by Newton's 3rd Law, the stepper motor must be exerting a steady torque on the inner gimbal the whole time it's on.

Yes or no: Is this not mechanically equivalent to the steady torque applied to the inner gimbal by Iacopo's test weight during steady precession of his gyroscope?

[ta0]

Oh! (Face palm!)  Of course, you are correct! In my head I had the idea that the flipping motors were stopping.

[Jeremy McCreary]

Should've thought to say this sooner department: Regarding the role of flywheel drag in the observed behavior of the LEGO demo...

In the video, this device generally operated at a steady equilibrium axial flywheel speed w_eq ultimately set by the applied spin-up motor voltages and the speed dependences of all the axial driving and braking torques involved. The main axial braking torque in this case being aerodynamic.

I see this kind of equilibrium between tops and electric starters all the time, no matter how dirty or streamlined. Ditto in electric fans.

Per Newton's 2nd Law, w_eq is the flywheel speed at which all the axial driving and braking torques cancel exactly -- leaving no net axial torque on the flywheel. Hence, no axial torque left to interact -- gyroscopically or otherwise -- with any of the transverse torques in the system.

Hence, flywheel drag can't affect the fundamental dynamic -- i.e., the qualitative motions observed. It can only affect the rates at which the fundamental dynamic unfolds -- and then only by limiting w_eq for a given choice of flywheel, spin-up motors, gearings, and applied voltages.

If you believe in Newton's Laws, there's no way around this.

[Iacopo]

Yes or no: Is this not mechanically equivalent to the steady torque applied to the inner gimbal by Iacopo's test weight during steady precession of his gyroscope?

Jeremy, you are right and I was wrong.  I looked at the video again, and I find that your explanation is perfect.
That in the video is a real torque induced precession, like in my gyroscope.