Non-Linear Analysis and Time Series Prediction of an Electrical Analogue of the Mechanical Double Pendulum

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In this paper the analogy between a mechanical double pendulum and an oscillating electrical system is presented. Instead of using analytic equations, we used the MultiSim circuit simulation environment in order to reproduce and interpret the response of the electrical oscillator. The electrical double pendulum presents a chaotic regime which is studied quantitatively by means of state space reconstruction. For this purpose the optimal delay time is calculated and the minimum embedding dimension is found with the method of False Nearest Neighbors. Using the reconstructed attractor and averaging over all neighbors' projections £-steps into the future, multistep ahead prediction achieved.