Phase portraits for parametrically excited pendula: An exercise in multidimensional data visualisation

Abstract

Data visualisation techniques are used to investigate the five dimensional phase space of a system of two pendula excited by an oscillatory force. A sequence of phase portraits is obtained that vividly illustrates the system undergoing a bifurcation as the frequency of the excitation is varied in a certain range. Such pictures provide valuable information on the topological transformations that the system undergoes as it approaches chaotic motion. This data visualisation method can also be applied to other multidimensional problems where a phase portrait analysis is helpful. © 1992.