Taking the derivative of S with respect to L yields the orbital equation derived above φ φ 0 = ∂ ∂ S ∂ ∂ L = ∂ ∂ S φ φ ∂ ∂ L + ∂ ∂ S r ∂ ∂ L = φ φ − − L 2 m ∫ ∫ r d r r 2 E t o t − − U ( r ) − − L 2 2 m r 2