Iacopo: Wonderful video. Thanks for sharing it.
I've been studying the behavior of high-CM tops using LEGO for a while now. The LEGO tops are only a few grams in total mass, but they show all the behaviors seen in the video, though at release speeds of ~5,000 to 9,600 RPM in my case. In particular, I see smooth descents like those at 5:18-6:12 and 15:45-17:02 and bucking descents (weak example at 10:05-10:35). The latter usually start out smooth, but the bucking keeps getting worse once it appears.
The smooth descents look to me to involve pure precession without nutation, while the bucking descents appear to develop nutation after spinning down a while. Reaching the critical spin rate for steady precession may have something to do with the onset of nutation, but tip radius of curvature is also involved.
The persistence of these behaviors over several orders of magnitude in mass confirms that they're largely driven by mass distribution. In my case, the ratio of axial moment of inertia (AMI) to transverse moment of inertia about the tip (TMI) seems to be an important controlling parameter. However, tip radius of curvature also plays an important role: The greater the radius, the slower the rotor's vertical descent, and the smaller the chance of seeing bucking on the way down.
I'll try to post video of some experiments with high-CM LEGO tops in the next few days. One nice thing about LEGO: I can change CM height, AMI, and tip radius of curvature at will. The TMI is hard to isolate, as it's inextricably tied to CM height by the parallel axis theorem (see Wikipedia).
ta0: Do you think that the precession in the video is still slow precession in the physics sense?