Stability study of a periodic system by a period-to-period mapping

摘要

Stability characteristics of period dynamical systems are investigated by the Poincaré map (point mapping) analysis approach. The approach is based on a method for obtaining an analytical expression for the period-to-period mapping description of the dynamics of the system and its dependence on system parameters. Stability and bifurcation conditions are expressed analytically and functional relations between various system parameters are determined. The approach is applied to investigate the parametric stability of a double pendulum. Excellent agreement with direct numerical results, assumed to be the “exact solution” for the purpose of this study, was obtained. Analytical stability studies of systems with multiple degrees-of-freedom is an important feature of the proposed approach since most existing analysis methods are applicable to single degree-of-freedom systems.