硬球与边界奇点的碰撞
Collision of a Hard Ball with Singular Points of the Boundary
摘要：
最近引入了物理台球，其中移动的粒子是硬球，而不是标准数学台球中的点。已经表明，在相同的台球桌上，物理台球可能具有与数学台球完全不同的动力学。如果台球桌的边界具有可见的奇点（如果台球桌是二维的，则为内角），即粒子可能与这些奇点碰撞，则会出现这种差异。在这里，我们考虑一个硬球与一个可见的奇点碰撞，并证明了与一个可见的奇点碰撞后的光滑球的运动确实是一个用于物理台球的研究。因此，这种碰撞等效于硬球的中心离开一个球的弹性反射，该球的中心在奇点，其半径与运动质点的半径相同。
英文摘要：
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.
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