A calculation method of grazing bifurcation point for period-1 orbit in
an impact oscillator with periodically moving borders <Abstract> This paper proposes a calculation method of the grazing bifurcation point in an impact oscillator with the periodically moving borders. First, we illustrate the behavior of the trajectory in an autonomous impact oscillator. Then, we define the composite Poincare map in order to discretize the system. Next, the condition of the grazing bifurcation is described as a simultaneous equation. Moreover, we show the Jacobian matrix to calculate the grazing bifurcation point numerically. Finally, the validity of our proposed method is confirmed by using a two-dimensional impact oscillator with the sinusoidally corrugated borders. |