Asymptotics of Maxwell time in the plate-ball problem

TL;DR

This paper investigates the asymptotic behavior of Maxwell time in the sphere rolling problem, providing estimates for small sinusoidal motions, which advances understanding of optimal contact trajectories.

Contribution

It introduces new asymptotic estimates for Maxwell time in the sphere rolling problem, specifically for small amplitude sinusoidal trajectories.

Findings

Two-sided estimate for Maxwell time asymptotics

Asymptotic analysis for small sinusoidal motions

Enhanced understanding of contact trajectory optimality

Abstract

The problem on rolling of a sphere on a plane without slipping or twisting is considered. One should roll the sphere from one contact configuration to another so that the length of the curve traced by the contact point in the plane was the shortest possible. Asymptotics of Maxwell time for rolling of the sphere along small amplitude sinusoids is studied. Two-sided estimate for this asymptotics is obtained.