Since these calculations are off-shell, one can equate the respective coefficients of ⁠ d q i ⁠, ⁠ d p i ⁠, ⁠ d t ⁠ on the two sides: ∂ ∂ H ∂ ∂ q i = − − ∂ ∂ L ∂ ∂ q i , ∂ ∂ H ∂ ∂ p i = q ˙ ˙ i , ∂ ∂ H ∂ ∂ t = − − ∂ ∂ L ∂ ∂ t .