Pieciewise Continuous Mappings derived from Parametrically Excited Pendulums

Abstract

This paper proposes a PCM method that is a method invoking Piecewise Continuous Map (PCM) to investigating nonlinear phenomena of oscillations in parametrically excited pendulums. At first, Sine Circle Map (SCM) is derived from the oscillations in the nonlinear oscillatory systems. Secondly, by applying least mean square method to SCM, approximate PCM is obtained. Fundamental properties of obtained PCM are shown to investigate the nonlinear phenomena in the oscillatory systems. Finally, the motions of mapped points in the PCM are investigated for various values of the parameters of the PCM. Furthermore, the relations of the PCM and the oscillations in the systems are shown for synthesis of the oscillatory nonlinear systems.