dH(qi,pi)=−∑i˙pidqi+∑i˙qidpi we have immediately the so-called canonical form of Hamilton’s equations of motion: \[\begin{align*} \dfrac{...dH(qi,pi)=−∑i˙pidqi+∑i˙qidpi we have immediately the so-called canonical form of Hamilton’s equations of motion: ∂H∂pi=˙qi∂H∂qi=−˙pi Evidently going from state space to phase space has replaced the second order Euler-Lagrange equations with this equivalent set of pairs of first order equations.
