In Hamiltonian mechanics, unlike Lagrangian mechanics which uses either all the coordinates or the momenta, the Hamiltonian equations of motion place coordinates and momenta on equal footing. For a system with Hamiltonian H (q, p, t), the equations are q ˙ ˙ i = ∂ ∂ H ∂ ∂ p i , p ˙ ˙ i = − − ∂ ∂ H ∂ ∂ q i .