The Geodesics of Rolling Ball Systems

Abstract

A well-known and interesting family of sub-Riemannian space are the systems involving two balls rolling against each other without slipping or twisting. In this note, we show how the sub-Riemannian geodesics of these space, when the two balls are embedded in ${\mathbb{R}}^3\times {\mathbb{R}}^3$, are horizontal curves on the intersections of these balls with Euclidean 5-planes.

6 pages, 0 figures

References in corpus (1)

• G2 and the Rolling Ball