论文标题
无滑动板的动力学
Dynamics of the no-slip Galton board
论文作者
论文摘要
理想的Galton板和Lorentz气台球模型已在数值和分析上进行了研究，主要是在忽略摩擦和旋转速度的设置中。我们消除了这些简化的假设，并研究了使用无滑碰撞的更通用模型的产生动力学，其中粒子旋转并在碰撞时可能在碰撞时交换线性和角动量，同时遵守某些保护定律。使用数值实验和相肖像分析，我们表明（与镜面分散台球相比），当引入小力量时（与镜面台球一致）在更强的力量新结构（包括不变区域）下引入小部队时，可能会持续存在。我们还分析地表明，随着外力周期性的引入，新型的周期性轨道在无力的情况下不存在。
The ideal Galton board and Lorentz gas billiard models have been studied numerically and analytically primarily in settings where friction and rotational velocity are neglected. We eliminate these simplifying assumptions and study the resulting dynamics of a more general model using no-slip collisions, in which particles rotate and may exchange linear and angular momentum at collisions while adhering to certain conservation laws. Using numerical experiments and phase portrait analysis we show that (in contrast to specular dispersing billiards) regularity persists when a small force is introduced while (consistent with specular billiards) under a stronger force new structure including invariant regions may arise. We also show analytically that with the introduction of an external force periodicity proliferates, with new types of periodic orbits not present in the no-force case.
