论文标题
旋转杆和球
Rotating rod and ball
论文作者
论文摘要
我们考虑一个机械系统，该系统由无限杆（直线）和平面上的球（无质点）组成。杆在其一个点之一周围均匀旋转。当与杆碰撞并在连续的命中之间自由移动时，球会弹性反射。还允许沿着杆的滑动运动。我们在特定时间内以给定的位置和速度证明了运动的存在和独特性。我们证明只有5种动议是可能的：台球动议；滑动运动；台球运动，然后滑动；滑动运动，然后是台球。当球位于旋转中心时，恒定运动。确定了连续命中和杆上击球点之间距离之间的时间间隔的渐近行为。
We consider a mechanical system consisting of an infinite rod (a straight line) and a ball (a massless point) on the plane. The rod rotates uniformly around one of its points. The ball is reflected elastically when colliding with the rod and moves freely between consecutive hits. A sliding motion along the rod is also allowed. We prove the existence and uniqueness of the motion with a given position and velocity at a certain time instant. We prove that only 5 kinds of motion are possible: a billiard motion; a sliding motion; a billiard motion followed by sliding; a sliding motion followed by a billiard one; and a constant motion when the ball is at the center of rotation. The asymptotic behaviors of time intervals between consecutive hits and of distances between the points of hits on the rod are determined.
