论文标题
引力场中的台球：抛物线和直角镜上弹跳的粒子
Billiards in a gravitational field: A particle bouncing on a parabolic and right angle mirror
论文作者
论文摘要
我们提出的几何工具适合研究均匀力场中台球轨迹的行为。考虑了两个示例：一个垂直平面，垂直平面在底部具有抛物线或直角边界。无论哪种情况，我们都会获得描述轨迹信封的方程式。这些方程与早期使用其他计算方法的方程非常吻合。此外，我们介绍了一些轨迹的新几何特性。我们表明，在抛物线边界的情况下，轨迹影响点的序列可以通过单个椭圆的多种反射来构建。
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.
