Scattering solution of a ball by a bat

TL;DR

This paper provides an exact mechanical solution for a ball-bat impact, accounting for friction and energy dissipation, and successfully matches experimental scattering data.

Contribution

It introduces a comprehensive rigid-body impact model that includes frictional and additional energy losses, with analytical solutions and experimental validation.

Findings

The model accurately predicts the ball's velocity and spin after impact.

Friction determines the impact dynamics independently of other energy losses.

The impact outcome depends on whether contact points slide or stick at separation.

Abstract

The problem of the mechanical evolution of a shock between a cylindrically symmetric bat and a spherical ball is solved in the strict rigid approximation for arbitrary values of the initial conditions. The friction during the impact is assumed to satisfy the standard rules. When the only source of energy dissipation is friction, the problem is fully solved by determining the separation point between the bodies. It also follows that whatever the character of any additional form of dissipation is, it only affects the ending value of the net impulse I done by the normal force of the bat on the ball at separation, but not the dynamical evolution with the value of I during the shock process. A relation determining whether the contact points of the two bodies slides between them or become at rest (to be pure rotation state) at the end of the impact, is determined for the case of the purely frictional energy dissipation. The solution is also generalized to include losses in addition to the frictional ones and then applied to the description of experimental measures of the scattering of a ball by a bat. The evaluations satisfactorily reproduce the measured curves for the output center of mass and angular velocities of the ball as functions of the scattering angle and the impact parameter, respectively.