755 強制力の作用する連成振子の非線形挙動(分岐・カオス)(OS.13 : 非線形現象の解明と応用)

概要

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Using the averaging method and Melnikov-type techniques, we study forced, coupled pendula and show that they exhibit very complicated dynamics. First, the averaged system for small oscillations of the pendula near the hanging state is analyzed. Codimension-one and -two local bifurcations at which several non-synchronized periodic and quasiperiodic orbits are born in the original system are detected. Moreover, the occurrence of the Shilnikov-type phenomena in the averaged systems, which yield chaotic motions in the original system, are shown. Similar analyses are also performed for small perturbations of periodic rotary orbits with no damping and external forcing. Finally, using a generalization of Melnikov method, we prove the occurrence of many other homoclinic phenomena, which also yield chaotic dynamics. We also give numerical simulation results to demonstrate our theoretical results.
一般社団法人日本機械学会の論文
2001-08-03