STABILITY STUDY OF A PERIODIC SYSTEM BY A PERIOD-TO-PERIOD MAPPING

Stability characteristics of period dynamical systems are investigated by the Poincare map (point mapping) analysis approach. The approach i s based on a method for obtaining an analytical expression for the per iod-to-period mapping description of the dynamics of the system and it s dependence on system parameters. Stability and bifurcation condition s are expressed analytically and functional relations between various system parameters are determined. The approach is applied to investiga te the parametric stability of a double pendulum. Excellent agreement with direct numerical results, assumed to be the ''exact solution'' fo r the purpose of this study, was obtained. Analytical stability studie s of systems with multiple degrees-of-freedom is an important feature of the proposed approach since most existing analysis methods are appl icable to single degree-of-freedom systems.