论文标题
引力台球在通用域内弹跳 - 焦点曲线和狭窄域
Gravitational billiards bouncing inside general domains -- foci curves and confined domains
论文作者
论文摘要
在恒定重力的影响下，巨大的粒子在某些功能$ f（x）$中描述的理想反射镜内弹跳。对于相关的飞行轨迹，我们得出了参数曲线，称为foci曲线。给定初始位置和能量的抛物线的所有焦点都位于这些曲线上。从这些焦点曲线中，相关的飞行抛物线包膜是在非周期性轨道情况下所有可能的粒子轨迹的密闭域中得出的，与镜面一起得出。对三个混凝土镜面表面进行简要讨论和可视化的一般结果。
A massive particle under the influence of a constant gravitational force that is bouncing inside an ideal reflecting mirror described by some function $f(x)$ is considered. For the associated flight trajectories we derive the parametric curves, named foci curves. All foci points of the parabolas for a given initial position and energy lie on these curves. From these foci curves the associated flight parabola envelopes are derived resulting, together with the mirror surface, in a confined domain for all possible particle trajectories in the non-periodic orbit case. The general results are briefly discussed and visualized for three concrete mirror surfaces.
