The second line implies that the specific angular momentum is conserved. We can then define an effective potential Φ Φ e f f = Φ Φ − − 1 2 r 2 θ θ ˙ ˙ 2 = Φ Φ − − h 2 2 r 2 and so : r ¨ ¨ = − − ∂ ∂ r Φ Φ e f f z ¨ ¨ = − − ∂ ∂ z Φ Φ e f f