Spinning Motion of Symmetric Top

Spinning Top Simulator with the sliding tip P of the spinning axis. Point P is subject to a resistive force proportional to its velocity $\vec v_P$ \[ \vec F = -k\, \vec v_P . \] Since P slides, the top loses energy through friction and the axis gradually tilts. However, since we assume a contact point with radius zero, there is no torque about the axis, so the spin speed $\omega_Z$ remains constant.

If the resistance coefficient $k$ is large, the tip P barely moves, and the motion resembles that of a fixed tip.

When $k$ is zero, there is no frictional force from the floor, and the center of mass G of the top remains stationary.

Compared to the case where the tip is fixed (see here), the major difference is that the nutation quickly damps out due to friction, and the motion naturally settles into steady precession.

Also, with the tip fixed, for a given spin speed $\omega_Z$ and tilt angle $\theta$, both slow and fast steady precession are possible. But this simulation shows that when the tip is not fixed, even if $k$ is large enough to make P almost stationary, fast precession is unstable and quickly converges to slow precession.

In actual tops where the tip is not fixed, when spun at high speed, not only nutation but also precession damps out, and the top seems to settle in an upright position. This behavior is not observed in this simulator, perhaps because the finite size of the tip is not considered. (see here),