An elementary treatment of the theory of spinning tops and gyroscopic motion, by Harold Crabtree.

ROTATION OF ANGULAR MOMENTUM

85

And, since OB' ==AA'=MFt, the change of angular momentum in time dt is MM2Qt about 0 Y... rate of change of angular momentum is M2 about Y.
This requires for its production a torque MQ about Y.
Hence (Fig. 44) if OL represents the momentum axis of a
top whose toe is the fixed point 0, the steady motion may be
discussed by considering that OL is rotated about OB, the perpendicular axis in the azimuthal plane, by the torque about O Y
perpendicular to the azimuthal plane. It will be noticed that
the gyroscopic resistance of the top to being turned about OY
is MQ (see Art. 45). P -41
Cor. If the axes of resultant angular momentum and angular
velocity be any two lines OP, OQ, the angular momentum and
velocity can each be resolved into components about OX, OY,
OZ and the torques producing the rotations of the component
momenta about the three axes can be separately found as above,
and equated to the corresponding components of the external
acting torques.
This method of determining the motion of a top is the one
most generally employed, since it is capable of easy extension
to the case where the motion is not steady.
86. The steady motion of a top spinning on a fine fixed point.
Consider the steady motion of a top spinning with its axle
inclined at an angle a to the vertical on a fine point 0 which is
Z
H
t< At-..<x.qzt?7ar m7omentun, rotatecd aboua OZ. \
FIG. 45.
fixed. An instance of such a motion will be that of a top
spinning on a table which is rough enough to prevent slipping,
while the toe is considered too fine for the friction to have a