(12)

With y = 0, (1), (2), (3) reduce to

u = −qz,   v = pz − rx,   w = qx;

(13)

and, denoting the radius of curvature of the meridian curve of the rolling surface by ρ,

dx= ρ cos θ dθ= −q ρ cos θ, dz= −ρ sin θ dθ= q ρ sin θ;
dt dtdt dt

(14)

so that

du= − dqz − q2ρ sin θ,
dt dt

(15)