Self-synchronized phenomena generated in pendulum-type oscillators (1st report, analysis for self-synchronized phenomena between two metronomes by using improved shooting method)

The self-synchronized phenomena between two metronomes fixed on the pendulum-like horizontal plate are investigated by applying the shooting method. The metronome system keeps the vibration under the effect of impulsive torque, but the ordinary shooting method is not applicable to such system. Therefore, the shooting method is improved to analyze the self-excited vibration generated by the impulsive effects. By applying the improved shooting method, the self-synchronized solutions of the metronome system are computed completely, and the stability of the solutions is also analyzed. From the computational results, the overall property of some types of self-synchronized vibration is clarified. In addition, Poincare maps, power spectrums and bifurcation diagrams confirm the occurrence of quasi-periodic vibrations and chaotic vibrations in the unstable regions.