Reconstruction of the Fourier expansion of a periodic force acting on an oscillator

Abstract

The problem of determining a periodic external force acting on a non-linear self-oscillating system of general type (the Li\'{e}nard oscillator) is considered. A procedure for the asymptotic estimation of the unknown coefficients in the partial sum of the Fourier series is proposed, which approximates the periodic disturbance of the oscillator on the basis of information about the motion of the original system. The procedure is based on the synthesis of invariant relationships; the method allows finding dependences between the variables on the trajectories of a specially constructed extended dynamic system and determining the sought unknown quantities as functions of known ones. The results of numerical simulation of the asymptotic estimation of external force parameters for the Duffing oscillator model are reported.