perhaps there is coupling between spin and wobble (nutation? as Iacopo suggests)
I am not sure about Alan's tops, but what I see in my tops I believe it is indeed nutation;
the following method is a more refined version I used for to recognize nutation from other kinds of wobbling:
some time ago Russpin gave an interesting formula for to know nutation speed;
for very little angles of tilting,
the proportion between spin speed and nutation speed is equal to the proportion between transverse moment of inertia and axial moment of inertia.A practical sample with numbers:
This is my top Nr. 15:
Axial moment of inertia: kg-m
2 0.0000765
Transverse moment of inertia: kg-m
2 0.0000429
Ratio between the two moments of inertia: 0.0000765 : 0.0000429 = 1.78
The transverse moment of inertia has to be measured at the tip. The trifilar pendulum measures it at the center of mass, not at the tip, anyway in this top the tip is really very close to the center of mass, so I didn't apply the parallel axis theorem.
I used the tachometer to know spin speed and nutation speed:
Spin speed: 247 RPM
Nutation speed: 415 RPM
Spin speed, second check: 229 RPM
Average between 247 and 229 is 238;
in the instant when nutation speed was at 415 RPM, spin speed was at about 238 RPM.
Ratio between the two speeds:
415 : 238 = 1.74
which is very near to the ratio between the two moments of inertia we have seen before, 1.78.
So we can see there is a correspondence.
This helps to make clear what is the kind of wobbling we can see in a top.
---------------------------------------------------------------------
I have nutation in my tops in three different situations:
- When the top is spun, usually there is at least a bit of nutation.
- When I kick the stem of the top with a finger while it is spinning. In these first two situations, nutation becomes weaker and weaker by the time, until disappearing completely; it takes some seconds up to some minutes for this to happen, depending on the kind of the top and the initial intensity of the nutation.
- When the contact point is large enough, (this happens when the tip is weared, after many hours of spinning, especially with ball tips), and especially if there is no lubricant. In this case the top starts nutating spontaneously at a certain speed, then it stops nutating spontaneously, a few minutes later, while the top continues spinning.
Some sort of "resonance effect" seems to trigger this effect, when the spin speed is favourable.
When the contact point is still larger, (tip badly weared), the top nutates for the whole duration of the spin.
Nutation is the only one reason I know for an intermediate peak wobbling.