Coefficient of Restitution as a Fluctuating Quantity

TL;DR

This paper investigates how the coefficient of restitution for a spherical particle varies with impact velocity, revealing non-Gaussian fluctuations and a probability distribution shaped by particle roughness affecting energy transfer.

Contribution

It introduces the concept of the coefficient of restitution as a fluctuating quantity and characterizes its probability distribution influenced by particle roughness.

Findings

Non-Gaussian fluctuations in restitution coefficient

Probability density formed by two exponential functions

Roughness affects energy transfer between degrees of freedom

Abstract

The coefficient of restitution of a spherical particle in contact with a flat plate is investigated as a function of the impact velocity. As an experimental observation we notice non-trivial (non-Gaussian) fluctuations of the measured values. For a fixed impact velocity, the probability density of the coefficient of restitution, $p(\epsilon)$, is formed by two exponential functions (one increasing, one decreasing) of different slope. This behavior may be explained by a certain roughness of the particle which leads to energy transfer between the linear and rotational degrees of freedom.