(4) du/dt - [theta]3v + [theta]2w = g[alpha] + X/M,
(5) dv/dt - [theta]1w + [theta]2u = g[beta] + Y/M,
(6) dw/dt - [theta]2u + [theta]1v = g[gamma] + Z/M,
and
(7) dh1/dt - [theta]3h2 + [theta]2h3 = yZ - zY,
(8) dh2/dt - [theta]1h3 + [theta]3h1 = zX - xZ,
(9) dh3/dt - [theta]2h1 + [theta]1h2 = xY - yX.
In the special case of the gyrostat where the surface is of revolution
round Gz, and the body is kinetically symmetrical about Gz, we take Gy
horizontal and Gzx through the point of contact so that y = 0; and
denoting the angle between Gz and the downward vertical by [theta]
(fig. 13)
(10) [alpha] = sin[theta], [beta] = 0, [gamma] = cos[theta].