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?