双侧约束对碰系统Lyapunov指数分析

Analysis of the Lyapunov exponential spectrum in a vibro-impact system with two-sided rigid stops

利用相对坐标和绝对坐标之间转换的思想,通过构建由流映射和局部映射所组成的Poincare映射,将非光滑连续动力系统转化成离散时间动力系统,计算两自由度双侧约束对碰系统的Lyapunov指数谱。将计算得到的系统Lyapunov指数谱与系统全局分岔图进行比较,证实计算Lyapunov指数谱方法的正确性。

By use of the transformation between relative coordinates and absolute coordinates presented here, Lyapunov exponential spectrum of a two-degree-of-freedom vibro-impact system with two-sided rigid stops was calculated by introducing Poincare mapping composed by flow mapping and local mapping and then changing a continuous-time dynamical system into a discrete-time one. Comparing the diagram of Lyapunov exponential spectrum obtained with the diagram of global bifurcation of the given system, the validity of the proposed method computing Lyapunov exponential spectrum was verified. Furthermore, some dynamical characters of this system under the given parameters were obtained.