完全非弹性蹦球倍周期运动的分形特征

一个落在振动台面上的完全非弹性球的运动是倍周期的.倍周期分岔过程受约化振动加速度的控制，倍周期分岔图由疏密相间的区域构成.在密集区内，倍周期分岔过程敏感地依赖于控制参数，呈现出复杂的几何结构.分析了密集区的分形特性，并计算了各密集区的分维数.结果表明密集区的分维数是依次增大的，逐渐趋于一个约为1.8的常数.关键词：蹦球倍周期分岔分形颗粒物质

Fractal characterization for subharmonic motion of completely inelastic bouncing ball

The motion of a completely inelastic ball dropped vertically on the vibrating table will undergo a series of subharmonic bifurcations, controlled solely by the normalized vibration acceleration. It has been shown that the bifurcation diagram for the ball' s motion consists of almost equally spaced dense regions, in which the bifurcation behavior is sensitively dependent on the control parameter. The dense regions have complex interior geometrical structures. Here they are treated as fraetal entities, and the fractal dimension for each of them is calculated. It is shown that the magnitude of the fractal dimension gradually increases, approaching a constant around 1.785.