(9)
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 θ (fig. 13)
α = sin θ, β = 0, γ = cos θ.
(10)
The components of angular momentum are
h1 = Ap, h2 = Aq, h3 = Cr + K,
(11)
where A, C denote the moment of inertia about Gx, Gz, and K is the angular momentum of a fly-wheel fixed in the interior with its axis parallel to Gz; K is taken as constant during the motion.
The axis Gz being fixed in the body,
θ1 = p, θ2 = q = −dθ/dt, θ3 = p cot θ.