Weakly non‐linear oscillator circuits and averaging: A general approach

Abstract The method of averaging has been used for years to prove the existence of oscillations in non‐linear circuits. In the past the application of averaging has tended to be ad hoc rather than systematic. In addition the validity of the method was not well established. the purpose of this paper is to rigorize and systematize the analysis of weakly non‐linear oscillator circuits via the method of averaging. In particular this paper will put on a rigorous foundation the work of Kuramitsu et al. 1‐3 on the ‘averaged potential’ and the work of T. Endo and others on the oscillatory modes of coupled oscillator circuits. Furthermore we give a novel way of simplifying the calculation of averages when we have a potential function representation.