I think that when the spindulum is spinning fast, the regular equations of a fast top apply.

I think I agree. As I already noticed with nutation, also with precession, the theoretical speeds seem not far from the measured ones, but only at high speed.

If I apply the formula:

Precession speed, (radians/sec) = [mass, (Kg) x gravity acceleration, (Kg m

^{2}) x CM-tip distance, (m)] : [axial moment of inertia, (Kg m

^{2}) x spin speed, (radians/sec)]

I get:

(0.036 x 9.8 x 0.003) : (0.0000127 x 30.7) = 2.7

30.7 x 9.55 = 293 RPM, spin speed

2.7 x 9.55 = 25.78 RPM, precession speed

which is consistent enough with the measured data in the graphic.

But at slow spin speed I get:

(0.036 x 9.8 x 0.003) : (0.0000127 x 4.2) = 19.8

4.2 x 9.55 = 40.1 RPM, spin speed

19.8 x 9.55 = 189 RPM, precession speed

which is quite far from the graphic data.

My idea is that there is something alterating the speeds of nutation and precession of the spindulums when the spin speed is slow.

This something could be the circular oscillation.

At slow spin speed, the circular oscilllation would still be present and deeply influence the speeds of the nutation and of the precession.

At the increasing of the spin speed, the circular oscillation would gradually fade away.

This would explain why the two curves of the nutation and of the precession in the graphic have the same dot of origin, and why this dot of origin also represents the natural oscillation frequency of the spindulum.