ベクトルを用いた区分線形系の解析方法

抄録

An analytical method based on vector fields is proposed for piecewise linear systems with singular regions or asymmetric restoring forces. By using matrix representation for these systems, state variables in each region can be explicitly expressed as a function of the time the orbit takes between two boundaries. The time can be determined by the Brent method, and periodic solutions can then be obtained. Furthermore, a new numerical technique to find explicit periodic solutions was developed, based on the Brent and Runge-Kutta-Gill methods. The validity of the proposed method is verified for three different 3-region systems by using the newly developed numerical method.