一个边界振荡的台球模型

A bouncing ball model with a oscillating border

研究了一种边界周期振荡的台球模型,使台球场在半圆和略小于半圆之间周期转换,解析地导出了描述这个经典台球系统动力学行为的映象方程.对台球仅在半圆和略小于半圆的台球场内无耗散运动的2种极端情况进行了解析与数值分析,说明这2种情况下台球都呈现典型的保守系统特征.初步数值研究表明,边界周期振荡的模型会显示耗散的特征.

This article suggests studying a bouncing ball model where a discontinuous borderline oscillates so that the poolroom periodically transfers between a semi-cycle and an even smaller one. The mappings, which describe the system's dynamics, have been deduced analytically. For the two extremities, i. e. the conservative motion of the classic particle inside the fixed semi-cycle and the smaller poolroom, the analytic and numerical investigation shows that typical conservative features are displayed. However, the first step investigation confirms that the border-oscillating model can display dissipative behavior, therefore it has the value for a further study.