Hamiltonian mechanics can be derived directly from Lagrange mechanics by considering the Legendre transformation between the conjugate variables (q,q˙,t) and (q,p,t) . Such a derivation is of consi...Hamiltonian mechanics can be derived directly from Lagrange mechanics by considering the Legendre transformation between the conjugate variables (q,q˙,t) and (q,p,t) . Such a derivation is of considerable importance in that it shows that Hamiltonian mechanics is based on the same variational principles as those used to derive Lagrangian mechanics; that is d’Alembert’s Principle and Hamilton’s Principle.
