Graduate Cause of upward motion of a nutating top

[Kashmir]

The locus of the rotational axis of a symmetrical rotating top with a fixed base is shown. This shows a nutation bounded by two circles.

What is the intuitive explanation as to why the top axis turns upwards at the lower circle and moves up? ( I understand the circular precession caused by gravity and would be grateful for an explanation only for the nutation).

Thank you :)

 

[Swamp Thing]

It depends on initial conditions. For any given angle wrt vertical, there is a matching precession rate that will involve no nutation, because the gyroscopic torque balances the gravity exactly. If the initial condition is of this sort, there will be no nutation.

On the other hand, if the precession rate is, say, higher than required to match the gravity, then the top will nutate upwards for a moment until the balance is achieved. However, it will overshoot the balance point due to inertia, and so an oscillation will be set up. So nutation is an oscillation around the angle at which gyro torque balances torque due to gravity -- an oscillation due to initial perturbation from the "neutral" angle.