Translational-Rotational Coupling during the Scattering of a Frictional Sphere from a Flat Surface

TL;DR

This paper investigates how rotational and translational energies couple during the collision of a sphere with a flat surface, using a frictional interaction model to analyze energy transfer mechanisms.

Contribution

It introduces an analytical model for translational-rotational coupling in sphere-surface collisions, highlighting energy transfer processes in frictional interactions.

Findings

Derived explicit expressions for energy transfer during collisions.

Identified conditions for energy conserving and dissipative collisions.

Provided analytical insights into rotational-translational energy coupling.

Abstract

At a macroscopic level, concepts such as top spin, back spin and rolling are commonly used to describe the collision of balls and surfaces. Each term refers to an aspect of the coupling of rotational motion during the collision of a spherical particle with a planar surface. In this paper we explore the mechanisms of energy transfer involving the collision of a rotating sphere and a surface using a model of frictional interactions developed for granular material. We present explicit analytical treatments for the scattering and derive expressions for two important limiting classes: energy conserving collisions and collisions subject to rapid transverse dissipation.