ABSTRACT
The aim of this section is to solve the fundamental problem of mechanics for a constrained system, namely the simple pendulum, by means of six different methods connected to: (i) classical (Newtonian) approach; (ii) Lagrange equations of the first kind; (iii) Lagrange equations of the second kind; (iv) Hamilton’s canonical equations; (v) the Hamilton-Jacobi formalism, and (vi) the action-angle formalism. This way, we shall put into evidence the resemblances and differences between these formalisms, on the one side, and show the generality and potency of the analytical formalism, as compared to the classical one, on the other.
