INVESTIGATION OF TRIPLE PENDULUM WITH IMPACTS USING FUNDAMENTAL SOLUTION MATRICES

Abstract

In this work a triple pendulum with damping, external forcing and impacts is investigated. We integrate the obtained system of governing equations between two successive impacts, and the discontinuity points are detected (by halving time step until the required precision is obtained). For each impact time, the state of the system is transformed using the extended restitution coefficient rule. The theory of Aizerman and Gantmakher is used to calculate the fundamental solution matrices in the analyzed system exhibiting discontinuities. Fundamental matrices are used during calculation of Lyapunov exponents, in stability analysis of periodic solution (Floquet multipliers) and in shooting method of finding periodic orbits. Then some examples for three coupled identical rods with horizontal barrier are shown.