Ω2 = dΩ1Ω2 − Ω1 dΩ2= Ω2ζ − (a2 + c2)(Ω1ξ + Ω2η) ζ,
dt dtdt (a2 − c2)

(24)

= ζ − (a2 + c2)·
N + a2 + c2
4c2
,
dt (a2 − c2)
M + (a2 + c2)2ζ2
2c2 (a2 − c2)

(25)

φ = ∫ ζ dζ a2 + c2
N + a2 + c2
4c2
· ζ dζ,
√Z a2 − c2
M + (a2 + c2)2ζ2
2c2 (a2 − c2)
√Z

(26)

which, as Z is a quadratic function of ζ2, are non-elliptic integrals; so also for ψ, where ξ = ω cos ψ, η = −ω sin ψ.

In a state of steady motion

= 0, Ω1= Ω2,
dt ξη

(27)