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

MOTION OF A GYROSCOPE

37

32. Distinction between axis and axle. The axis of symmetry
of a solid of revolution we shall in general call its axle, as
distinguished from any other axis in the body about which it
may be rotating or have a component rotation.
It should be noticed that the axle in this sense is a geometrical
straight line-not a thick spindle relative to which, or fixed
to which, the body rotates.
33. Definitions. Gyrostat. A solid of revolution which is
capable of rotation about a straight rod coincident with the
axis of the solid is frequently called a gyrostat.
Gyroscope. A gyroscope is an instrument in which a gyrostat
is mounted in a frame. The most common form of a gyroscope
is that in which the frame is so mounted that the gyrostat can
turn in anxy direction. See Figs. xxII. sqq.
We shall, however, in general refer to the spinning wheel of
the instrument as "the gyroscope."
Spin of a gyroscope. By the spin of a gyroscope or top about
its axle we mean the total angular velocity about the line fixed in
space with which the axle happens to be coinciding at the instant
in question. It is not the angular velocity relative to the frame.
X R
FIG. 19. FIG. 20.
34. Motion of a gyroscope with its axle horizontal. By
means of the parallelogram of angular momenta we can discuss
FIG. 19. FIGS. 20.
34. Motion of a gyroscope with its axle horizontal. By
means of the parallelogram of angular momenta we can discuss
the motion of a gyroscope which is moving, under the action
of gravity only, about the fixed vertical through its point of
support with its axle horizontal as in Fig. 19.