Now, the total differential of the momentum space Lagrangian L ′ is d L ′ = ∑ ∑ i = 1 n ( ∂ ∂ L ′ ∂ ∂ p i d p i + ∂ ∂ L ′ ∂ ∂ p ˙ ˙ i d p ˙ ˙ i ) + ∂ ∂ L ′ ∂ ∂ t d t so by comparison of differentials of the Lagrangians, the momenta, and their time derivatives, the momentum space Lagrangian L ′ and the generalized coordinates derived from L ′ are respectively L ′ = L − − ∑ ∑ i = 1 n ( q i p ˙ ˙ i + q ˙ ˙ i p i ) , − − q ˙ ˙ i = ∂ ∂ L ′ ∂ ∂ p i , − − q i = ∂ ∂ L ′ ∂ ∂ p ˙ ˙ i .