两球弹跳问题中的延迟篮板
Delayed Rebounds in the Two-Ball Bounce Problem
摘要：
在一个网球落在篮球上的课堂演示中，网球惊人的高反弹通常是用弹性碰撞的动量守恒来解释的，篮球与地板的碰撞被视为独立于两个球之间的碰撞。通过引入恢复恢复系数，将这一教科书式的解释推广到非弹性碰撞。这种独立的接触模型（ICM），在本文中审查，是准确的各种情况下，即使碰撞不是真正独立的。然而，探索ICM无法解释的情况是很容易的，例如将网球换成乒乓球。在本文中，我们研究的条件，导致一个“延迟反弹效应”，一个小的第一次反弹，其次是一个更高的第二次反弹，使用技术访问一个本科生。动力学模型是基于常见的阻尼谐振子的解决方案。我们专注于使运动方程无量纲的数值模拟，并减少参数和初始条件的数量，以强调普遍的行为。延迟反弹效应被发现的参数范围内，最常见的情况下，第一次反弹低于ICM预测。
英文摘要：
In the classroom demonstration of a tennis ball dropped on top of a basketball, the surprisingly high bounce of the tennis ball is typically explained using momentum conservation for elastic collisions, with the basketball-floor collision treated as independent from the collision between the two balls. This textbook explanation is extended to inelastic collisions by including a coefficient of restitution. This independent contact model (ICM), as reviewed in this paper, is accurate for a wide variety of cases, even when the collisions are not truly independent. However, it is easy to explore situations that are not explained by the ICM, such as swapping the tennis ball for a ping-pong ball. In this paper, we study the conditions that lead to a "delayed rebound effect," a small first bounce followed by a higher second bounce, using techniques accessible to an undergraduate student. The dynamical model is based on the familiar solution of the damped harmonic oscillator. We focus on making the equations of motion dimensionless for numerical simulation, and reducing the number of parameters and initial conditions to emphasize universal behavior. The delayed rebound effect is found for a range of parameters, most commonly in cases where the first bounce is lower than the ICM prediction.
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