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

88

GYROSCOPIC RESISTANCE

round which the angular momentum Cw sec y is rotated with
velocity 0 sin (a- y).
z A,/
IG L 46.
C Msecy si(-y)Mgasin,
CcQ(sin a- - cos a. tan y)-gt sin a,
f//
I ', / torque
\G 90. We see (Fig4. 4)
We that the velocity axis is
s y / /( in this case the instana(sin a a taneou axisi and makes
a constant angle (a-)
exprswith the vertical OZ: it
\ vS/// therefore describes a cone
\< / Ab ed i~r spare having Z
It is also inclined to
FI. 46. s g
and thus describes a cone fixed %in the body having OG as
We have, employing right-handed rotations,
GCo sec y. li sin (a - y) = Jga sin a,
Co] 2(sin a - cos a. tan y)= Mgca sin a,
or Gow2 Qsin a-cos aAQi ta) eMga sin a,
i.e. 6CffQ- Al2cos a = Mga, as before.
It will be noticed that the first of the above equations
expresses the fact that
Za the gyroscopic resistance
is equal to the external
torque.
F.G 90. We see (Fig. 46)
\(,, / that the velocity axis is;. ^j\/\,/ in this case the instantaneous axis, and makes
a constant angle (a- f3)
with the vertical OZ: it
therefore describes a cone
andx thus defixed in space having OZ
axis and vertical angle 2,3.