A Minimalist Approach to Rolling Wheels
Classical Analysis and ODEs
2026-05-15 v3
Abstract
In 1960, G. B. Robison discovered the general equations relating roads and wheels, where either can have an unusual shape (e.g., the square wheel rolls smoothly on a catenary). But he used some inobvious assumptions regarding the meaning of rolling. Here we derive the equations for the road appropriate for a given wheel using only the single assumption that rolling occurs with no slipping. We do not require that the wheel be differentiable, so this allows the construction of a wheel-road pair when the wheel is a continuous nowhere differentiable function.
Cite
@article{arxiv.2604.03749,
title = {A Minimalist Approach to Rolling Wheels},
author = {Antonín Slavík and Stan Wagon},
journal= {arXiv preprint arXiv:2604.03749},
year = {2026}
}
Comments
11 pages, 19 figures