On a variant of the asymptotic procedure (for weakly nonlinear autonomous systems)
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 . 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.
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