Abstract
The resonant oscillations of a linear system, driven by a nonlinear forcing term of quite a general type, are here treated mainly by the Hamiltonian formalism, starting from the Krylov-Bogoliubov approximate solutions. From the review of many practical examples, this work evolves till the attainment of complete and general solutions, through a proper framing of these examples in the Hamilton formalism. Beyond several original calculations, some ultimate demonstrations, regarding a few particular cases of separatrix curves, are performed.
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