For fast spin
One solution to the above equation is
This motion is
known as precession.
Precession occurs in the presence of an applied couple and occurs at a
slow rate in comparison to the rate of spin.
Another root of the equation for fast spin is given by
This motion occurs at a constant rate even when the applied couple is
zero. This motion is called nutation.
Video of nutation
a gyroscope is released from rest as in the
above video cupsidal
is observed. The motion is depicted in the figure below
During this motion moment
is conserved about the vertical axis (assuming frictionless bearings)
.The component of moment of momentum about the vertical axis is zero to
start with and so remains zero during the motion. During the motion the
loss in potential energy is balanced by a gain in potential energy.
can be seen to be a damped motion and after a while the observed
oscillations die away. The angle of steady precession is equal