引力场中的台球：一个粒子在抛物面和直角镜上弹跳
Billiards in a gravitational field: A particle bouncing on a parabolic and right angle mirror
摘要：
我们提出的几何工具，是适合于研究的行为的台球轨迹在一个均匀的力场。两个例子被认为是：一个垂直的平面与开放的顶部和抛物线或直角边界在底部。在任何一种情况下，我们都得到了描述轨迹包络的方程。这些方程与以前用其他计算方法得到的方程吻合得很好。此外，我们提出了一些新的几何性质的轨迹。我们表明，在抛物线边界的情况下，可以很容易地构建一个单一的椭圆的多次反射的轨迹的影响点的序列。
英文摘要：
We propose geometric tools that are suitable for studying the behavior of a billiard trajectory in a homogeneous force field. Two examples are considered: a vertical plane with an open top and with a parabolic or right angle boundary at the bottom. In either case, we obtain equations that describe the envelope of a trajectory. These equations are in good agreement with those found earlier with the use of other calculation methods. In addition, we present some new geometric properties of trajectories. We show that in the case of a parabolic boundary the sequence of the trajectory impact points can be easily constructed by multiple reflections of a single ellipse.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
