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

CHAPTER VI.
STEADY MOTION OF A TOP.
75. The student is reminded at the commencement of this
chapter that, when a solid body is under consideration,
(i) Angular velocity about any line means total angular
velocity-not relative to some moving plane, unless
this is expressly stated.
(ii) Angular velocity about a line which is moving means
(total) angular velocity about the line fixed in space,
with which the moving line happens to be coinciding
at the instant in question.
76. In the preceding chapter the bodies whose rotation we
have discussed have been symmetrical bodies, as, for example,
a fly-wheel; and all the rotations have been about an axis of
symmetry, i.e. the axle. If the axis were not an axis of
symmetry, an angular velocity about this axis would in general
involve angular nomentumn (about this axis, and also) about
the two axes perpendicular to it, as is shown in the next article.
In this chapter we propose to discuss the equations of motion
of an ordinary spinning top, in which case it is clear that only
the axle of the top is an axis of symmetry, and any other axis
is not. But we shall see in Art. 79 that, since the top is a solid
of revolution, any axis perpendicular to the axle of the top is
the same for our purpose as if it were an axis of symmetry,
and angular velocity about such an axis involves (of course
angular momentum about that axis, but) no angular momentum
about perpendicular eaxes.
77. Rotation about one axis involves in general angular
momenta about other axes at right angles to the first. In
general, if a body has at any instant an angular velocity about
a given axis, this velocity involves an angular momentum about
each of two lines perpendicular to the original axis and to
each other.
For let OZ be the original axis of rotation about which the
body has an angular velocity in the positive direction.
Let OX, OY, be two straight lines perpendicular to OZ and
to each other.