On the calculus of variations: opening simpler, direct routes

We first offer a direct, analytic way of deriving the Euler equation. The method we suggest avoids the difficulties met by Lagrange, which become serious in the case of complex func-tionals. It also leads to the new Hamiltonian, defined by Robert Dorfman; in turn, this Hamiltonian can be extended to high order functionals or n–fold integrals, thus providing, almost immediately, the corresponding Euler equations.