Some Notes on an Approximate Solution for the Free Oscillation Characteristics of Non-Linear Systems Typified by x + F (x, x) = 0

摘要

A modified form of the approximate method developed by Karloff and Bogoliuboff is derived and applied to particular cases with a large frequency dependence on amplitude. The results suggest that some relaxation of the constraints of the earlier method may be justified.nThe method provides an approximate solution of the frequency and the amplitude damping envelope in terms of the amplitude, and suggests itself as a means of cataloguing, in matrix form, the characteristics of practical non-linear systems.