Three Balls Problem Revisited - On the Limitations of Event-Driven Modeling

TL;DR

This paper revisits the three balls problem, revealing that simple models often overlook complex collision scenarios that significantly affect the outcome, especially in elastic collisions.

Contribution

It demonstrates that the common textbook explanation is an oversimplification and highlights the importance of considering multiple collisions for accurate modeling.

Findings

Multiple collisions can drastically alter final velocities.

Simple models may underestimate the complexity of elastic collisions.

Complex collision scenarios are crucial for accurate predictions.

Abstract

If a tennis ball is held above a basket ball with their centers vertically aligned, and the balls are released to collide with the floor, the tennis ball may rebound at a surprisingly high speed. We show in this article that the simple textbook explanation of this effect is an oversimplification, even for the limit of perfectly elastic particles. Instead, there may occur a rather complex scenario including multiple collisions which may lead to a very different final velocity as compared with the velocity resulting from the oversimplified model.