And thus : δ δ r ¨ ¨ = − − ∂ ∂ r 2 Φ Φ e f f δ δ r = − − Ω Ω r 2 δ δ r δ δ z ¨ ¨ = − − ∂ ∂ r 2 Φ Φ e f f δ δ z = − − Ω Ω z 2 δ δ z We then note κ κ 2 = Ω Ω r 2 = ∂ ∂ r 2 Φ Φ e f f = ∂ ∂ r 2 Φ Φ + 3 h 2 r 4 In a circular orbit h c 2 = r 3 ∂ ∂ r Φ Φ . Thus : κ κ 2 = ∂ ∂ r 2 Φ Φ + 3 r ∂ ∂ r Φ Φ The frequency of a circular orbit is Ω Ω c 2 = 1 r ∂ ∂ r Φ Φ which finally yields : κ κ 2 = 4 Ω Ω c 2 + 2 r Ω Ω c d Ω Ω c d r