Abstract
In this paper, periodic motions in a periodically forced, damped double pendulum are analytically predicted through a discrete implicit mapping method. The implicit mapping is developed from discretization of the corresponding differential equation. From the mapping structures, period-1 to period-4 motions are obtained and the corresponding stability and bifurcation analysis of the periodic motions are completed through eigenvalue analysis. Using the finite Fourier series, nonlinear frequency-amplitude characteristics of period-1 to period-4 motions are presented. Numerical simulations of period motions in the double pendulum is completed, and the initial conditions are obtained from the analytical predictions. The harmonic amplitude spectrums are also presented for showing harmonic term effects on periodic motions.
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