\displaystyle \varepsilon H=p(t)\big (q(t+\varepsilon )-q(t)\big )-\varepsilon L and 𝑝 = ∂ 𝐿 ∂ 𝑞 ˙

\displaystyle \varepsilon H=p(t)\big (q(t+\varepsilon )-q(t)\big )-\varepsilon L and 𝑝 = ∂ 𝐿 ∂ 𝑞 ˙ , where the partial derivative with respect to 𝑞 ˙\displaystyle \dot q holds q(t + ε) fixed. The inverse Legendre transform is 𝜀 𝐿 = 𝜀 𝑝 𝑞 ˙ − 𝜀 𝐻 , \displaystyle \varepsilon L=\varepsilon p\dot q-\varepsilon H where 𝑞 ˙ = ∂ 𝐻 ∂ 𝑝