A COMMENT ON THE NATURAL FREQUENCY ANALYSIS OF NON-LINEAR SYSTEMS

A linearization analysis, an approximate nonlinear analysis, and an exact analysis for nonlinear systems are presented and illustrated by means of a pendulum problem. The natural frequencies and stability predicted by the three analyses are compared. It is shown that the prediction of the natural frequency and the stability of nonlinear systems can be significantly improved by an approximate, nonlinear model, and that the usual linearization analysis can give misleading results for nontrivial equilibria or initial states. (CSA)