三体衝突振動系における定常衝突解の安定性とその操作
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概要
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By adding impulse excitation and energy dispersion operations to time evolution of Patel's vibro-impact system, we can obtain steady states of three-body vibro-impact system with two small oscillators coupled to one large oscillator under wave algorithm. In this study, we proved that the steady states are stable limit-cycles by using state transition matrix. When small deviations of parameters exist, we observed the convergence of state vectors under the various conditions of the system in state transition diagram. Because this cycle is stable, we can control a collision velocity arbitrarily by changing the amount of excitation. In case the collision position shifts to the direction of the balance point, convergence time is shortened by increasing the amount of excitation. We obtained the optimal division number of excitation from the approximated state transition matrix and numerical calculations. Because the convergence time is minimized in the optimal division number of excitation, we can smoothly control the steady vibro-impact oscillation of tapping mode AFM and can smoothly operate the manipulator in space.