The method of coordinate averaging

In this paper a perturbation technique for nearly linear oscillatory systems is developed and a set of second order averaged equations is obtained. The standard form treated is $\text{dx}\text{dt}\text{=}\text{F}\text{(}\text{x, t}\text{; ?), |?| ? 1}$, and a well known example is considered in detail so as to show how the asymptotic approximations of other methods can be obtained.