One may now equate these two expressions for ⁠ d H ⁠, one in terms of ⁠ L ⁠, the other in terms of ⁠ H ⁠ : ∑ ∑ i ( − − ∂ ∂ L ∂ ∂ q i d q i + q ˙ ˙ i d p i ) − − ∂ ∂ L ∂ ∂ t d t = ∑ ∑ i ( ∂ ∂ H ∂ ∂ q i d q i + ∂ ∂ H ∂ ∂ p i d p i ) + ∂ ∂ H ∂ ∂ t d t .