Impedance of rigid bodies in one-dimensional elastic collisions

TL;DR

This paper introduces a novel approach to analyzing one-dimensional elastic collisions of rigid bodies by applying the concept of impedance matching, typically used in oscillatory systems, to understand energy transfer efficiency.

Contribution

It extends the concept of impedance to rigid body collisions and offers a new framework for analyzing maximum energy transfer in elastic collisions.

Findings

Mass of the body acts as a measure of impedance.

Maximum energy transfer corresponds to impedance matching.

Framework bridges elastic collision analysis with impedance concepts.

Abstract

In this work we study the problem of one-dimensional elastic collisions of billiard balls, considered as rigid bodies, in a framework very different from the classical one presented in text books. Implementing the notion of impedance matching as a way to understand eficiency of energy transmission in elastic collisions, we find a solution which frames the problem in terms of this conception. We show that the mass of the ball can be seen as a measure of its impedance and verify that the problem of maximum energy transfer in elastic collisions can be thought of as a problem of impedance matching between different media. This approach extends the concept of impedance, usually associated with oscillatory systems, to system of rigid bodies.