The velocity of H is in the direction KH perpendicular to the plane COC′, and equal to gMh sin θ or An2 sin θ, so that if a point in the axis OC′ at a distance An2 from O is projected on the horizontal plane through C in the point P on CK, the curve described by P, turned forwards through a right angle, will be the hodograph of H; this is expressed by
| An2 sin θ e(ψ + 1/2π)i = iAn2 sin θ eψi = | d | (ρeῶi) |
| dt |
(3)
where ρeῶi is the vector CH; and so the curve described by P and the motion of the axis of the top is derived from the curve described by H by a differentiation.
Resolving the velocity of H in the direction CH,
d·CH/dt = An2 sin θ sin KCH = An2 sin θ KH/CH,
(4)
d·½CH2/dt = A2n2sin θ dθ/dt.
(5)