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Published in:
2022 | OriginalPaper | Chapter
9. Periodic Motions and Bifurcations in a Double Pendulum
Authors : Chuan Guo, Albert C. J. Luo
Published in: Dynamics and Fault Diagnosis of Nonlinear Rotors and Impellers
Publisher: Springer International Publishing
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Abstract
In this chapter, period-1 to period-4 motions and an independent period-3 motion of a periodically forced double-pendulum are predicted through a discrete implicit mapping method. The corresponding stability and bifurcation of periodic motions are determined through eigenvalue analysis. Numerical simulations of the periodic motions in the double-pendulum system is completed for verification of analytical predictions. The harmonic terms effects on periodic motions were presented through the harmonic amplitude spectrums. For such a study, the pendulum is not expanded through the Taylor series expansion, and many higher-order harmonic terms are involved to make periodic motions complicated, which cannot be obtained from the perturbation analysis.