New constructive methods for analysis of resonant systems

The modern theory of perturbations, based on the Krylov–Bogolyubov method [1], has two essential advantages: the determination of the iterations does not require the preliminary solution of the generating equation and the choice of the initial conditions, which for every approximation minimizes the difference “exact solution minus asymptotic solution”. The algorithm of constructing the perturbed solution may be realized with computer algebra methods.