(17)
can be expressed, when normalized by the factor √(z1 − z3)/2, by the inverse elliptic function in the form
| mt = ∫ zz3 | √ (z1 − z3) dz |
| √ [4 (z1 − z) (z2 − z) (z − z3)] |
| = sn−1 √ | z − z3 | = cn−1 √ | z2 − z | = dn−1 √ | z1 − z | . |
| z2 − z3 | z2 − z3 | z1 − z3 |
(18)
z − z3 = (z2 − z3) sn2mt, z2 − z = (z2 − z3) cn2mt, z1 − z = (z1 − z3) dn2mt.
(19)
z = z2sn2mt + z3cn2mt.
(20)
Interpreted dynamically, the axis of the top keeps time with the beats of a simple pendulum of length