(13) u = -qz, v = pz - rx, w = qx;
and, denoting the radius of curvature of the meridian curve of the
rolling surface by [rho],
dx d[theta]
(14) -- = [rho] cos[theta] -------- = -q [rho] cos[theta],
dt dt
dz d[theta]
-- = -[rho] sin[theta] -------- = q [rho] sin[theta];
dt dt
so that
du dq
(15) -- = - -- z - q^2[rho] sin[theta],
dt dt
dv dp dr
(16) -- = -- z - -- x + pq[rho] sin[theta] + qr[rho] sin[theta],
dt dt dt
dw dq
(17) -- = -- x - q^2[rho] cos[theta].
dt dt