with θ measured from the upward vertical, and
A sin2 θψ + CR cos θ = G,
(19)
where A now refers to a transverse axis through the centre of gravity. The elimination of ψ leads to an equation for z, = cos θ, of the form
| ( | dz | ) | 2 | = 2 | g | Z | = 2 | g | (z1 − z) (z2 − z) (z3 − z) | , | ||
| dt | h | 1 − z2 + A/Mh2 | h | (z4 − z) (z − z5) |
(20)
with the arrangement
z1, z4 > / > z2 > z > z3 > − / > z5;
(21)
so that the motion is hyperelliptic.