论文标题
硬球的碰撞与边界的奇异点
Collision of a Hard Ball with Singular Points of the Boundary
论文作者
论文摘要
最近引入了物理台球，其中移动粒子是硬球，而不是标准数学台球中的点。已经表明，在同一台球表中，物理台球可能与数学台球完全不同。如果台球表的边界具有明显的奇异性（如果台球表为二维），则会出现这种差异，即粒子可能与这些奇异点相撞。在这里，我们考虑了一个坚硬的球的碰撞，可见的奇异点，并证明与可见的单数点相撞后光滑球的运动确实是在物理台球研究中使用的。因此，这种碰撞等同于在单个点处的中心与中心相同的半径与移动粒子的半径相同的弹性反射。
Recently were introduced physical billiards where a moving particle is a hard sphere rather than a point as in standard mathematical billiards. It has been shown that in the same billiard tables the physical billiards may have totally different dynamics than mathematical billiards. This difference appears if the boundary of a billiard table has visible singularities (internal corners if the billiard table is two-dimensional), i.e. the particle may collide with these singular points. Here, we consider the collision of a hard ball with a visible singular point and demonstrate that the motion of the smooth ball after collision with a visible singular point is indeed the one that was used in the studies of physical billiards. So such collision is equivalent to the elastic reflection of hard ball's center off a sphere with the center at the singular point and the same radius as the radius of the moving particle.
