Yes you're right, I'd made a mistake when calculating it before. And yes, both the rates I get are definitely precession rates.
I asked one of my lecturers about this problem today, and he explained it all to me. Both precession rates exist, and the top can stably precess at either one of...
When you have a spinning top undergoing forced precession (due to the torque created by its weight trying to tip it), you seem to get two precession rates. Why?
I get this result from using Euler's equations, specifically that the sum of moments tipping the top is (in the case of steady...