So the constant H ′ can be used to change time derivatives along the orbit to partial derivatives with respect to θ θ at constant J. Differentiating the integral for J with respect to J gives an identity that fixes H ′ : d J d J = 1 = ∫ ∫ 0 T ( ∂ ∂ p ∂ ∂ J d x d t + p ∂ ∂ ∂ ∂ J d x d t ) d t = H ′ ∫ ∫ 0 T ( ∂ ∂ p ∂ ∂ J ∂ ∂ x ∂ ∂ θ θ − − ∂ ∂ p ∂ ∂ θ θ ∂ ∂ x ∂ ∂ J ) d t .