对称耦合双振子的复杂运动

Complex movement in 2-space of a doubly asymmetric coupled spring

建立了一个双弹簧对称耦合的振子系统.计算了通过升维降阶技术得到的一个等价系统的Lyapunov指数,表明振子的运动或为混沌或为准周期.振子中没有引入能量耗散,其运动轨迹因初始条件不同而有很大不同.最后指出,判断这样的系统性态,唯一可靠的方法是计算Lyapunov指数.

A system formed by two springs coupled asymmetrically is suggested. The Lyapunov expo- nent is calculated in anquivalent system obtained by an increasing dimension and reducing order method. It indicates that the system is chaotic or quasi-periodic in the majority region of the controlled parameter, the elastic coefficient. The trajectories of system bear typical characteristics of a conservative system, that is, one trajectory corresponds uniquely to one set of initial conditions. It should be pointed out that the nature of such coupled oscillators can be revealed only by lyapunov exponent.