An effective method for calculating the grazing bifurcation points in an impact oscillator
Yusho Shimizu, Hiroo Sekiya, Kazuyuki Aihara, and Takuji Kousaka
IEICE Technical Committee on Nonlinear Problems, vol.111, no.339, pp.31-34, Dec., 2011. [pdf document]

<Abstract>

In recent years, researchers have proposed some calculating methods of the grazing bifurcation points. However, the composition of the Jacobian matrix is complicated, because these methods treat the periodic time of the solution as a dependent variable. This paper proposes an effective method for calculating the grazing bifurcation points in an impact oscillator. Our method has the property that the periodic time is treated as an independent variable. First, we explain the dynamical system. Next, we show the calculating method of the grazing bifurcation points by using some conditional equations. Finally, we apply the method to Rayleigh-type equation and confirm the validity of our method.