On a variant of the asymptotic procedure (for weakly nonlinear autonomous systems) - Dinh, Nguyen Van (Vietnam Journal of Mechanics, 2003)
As well-known, usually, in the asymptotic (Krylov-Bogoliubov-Mitropolski) method, the full amplitude (a) of the first harmonic is used as variable in asymptotic expansions [1]. In the first approximation, the equations of stationary oscillations are rather simple, however, in higher approximation, these equations often become very complicated, especially when initial conditions are imposed.