| Ω2 | dφ | = | dΩ1 | Ω2 − Ω1 | dΩ2 | = Ω2ζ − | (a2 + c2) | (Ω1ξ + Ω2η) ζ, |
| dt | dt | dt | (a2 − c2) |
(24)
| dφ | = ζ − | (a2 + c2) | · |
| , | |||
| dt | (a2 − c2) |
|
(25)
| φ = ∫ | ζ dζ | − | a2 + c2 | ∫ |
| · | ζ dζ | , | |||
| √Z | 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
| dζ | = 0, | Ω1 | = | Ω2 | , |
| dt | ξ | η |
(27)