In this article we have two objectives. The first is to present the general problem of the lagrangean mechanics and the Hamilton principle by using mathematical definitions of functional directional derivatives and critical or stationary points of a functional. The second is to analyse, by use of the functional derivative of second order, conditions where the solutions of unidimensionals models represent minimum, of saddle or maximum local points of the action functional and show some examples.
Functional directional derivative; stationary point of a functional; Euler-Lagrange equation; functional derivative of second order
