For a gyrostat spinning upright on the summit of a sphere of radius b, the signs of a and b must be changed in (5), or else the sign of g, which amounts to the same thing.
Denoting the components of horizontal displacement of the point of the fly-wheel by ξ, η, then
br = ξ, bs = η, bσ = ξ + ηi = λ (suppose),
(10)
ω = αῶ + λ.
(11)
If the point is forced to take the motion (ξ, η, ζ) by components of force X, Y, Z, the equations of motion become
−Aq + Kp = Ya − Zaq,
(12)
Ap + Kq = −Xa + Zap,