AN ALTERNATIVE APPROACH TO POINCARÉ SECTIONING IN WEAKLY NONLINEAR SYSTEMS

Abstract

A large array of dynamical systems can be broadly classified as weakly nonlinear, where a common feature is the presence of dual time-scale dynamics. Often it is desirable to isolate the dynamics at one time scale (typically the slower time scale), and this paper presents a generic phase-sensitive detection method that successfully isolates the slow-time dynamics, stripping off the less-relevant and often dominant fast-time dynamics. We shall also show for the first time, under certain phase considerations, the equivalence of the present method and the traditional Poincaré section of the original full response. The method is first presented in theory and then applied to data from a numerical simulation of the forced spherical pendulum followed by data from a similar spherical pendulum experiment. The method is successful provided certain conditions apply for phase stationarity.