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

82

STEADY MOTION

81. Moving axis. It is sometimes convenient to resolve the
angular velocity of a rotating body about three axes mutually
at right angles, and these three axes form a frame of reference,
which may itself perhaps be moving.
If we know the motion of the body relative to this frame,
and the motion of the frame, we know the motion of the whole
body.
If the frame of reference is moving, the axes are called
moving axes, and the frame does not necessarily carry the
body with it, for all the axes are not necessarily fixed in the
body, but may be passing through it.
82. The velocities and momenta of a spinning top in steady
motion. By the stead of a top is meant the motion
in which the angular velocity w about the axle of the top
remains constant, while the axle has a constant inclination a to the
vertical, and is carried round the vertical with constant angular
velocity Q (Fig. 40). This velocity Q is called the azijhl
veloci the vertical plane AGZ through the axle o the top
e-ng called the azimuthal plane. During steady motion, the
centre of gravity G describes a horizontal circle. The lines GC,
GA, of which GA is always moving through the material of
the top but remaining with GC in the azimuthal plane, are
taken as moving axes of reference.
Z! I
FIG. 40. FIG. 41.
The velocities. The angular velocity Q2 of the azimuthal plane
about ZG (or -Q about GZ, Art. 20), can be resolved (Fig. 41)
into (a) Q sin a about GA,

(b) Q cos a about GC.