The Geodesics of Rolling Ball Systems

2012/08/28 by Daniel R. Cole, Cole, Daniel R.
Mathematics · Physics and Astronomy · #53C17 53C22 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #math.DG #msc:53C17 #msc:53C22

paper · pdf · doi:10.48550/arxiv.1208.5555

6 pages, 0 figures

arxiv created 2012/08/28 · openalex publication_date 2012/08/28 · arxiv updated 2012/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 ℝ³ × ℝ³, are horizontal curves on the intersections of these balls with Euclidean 5-planes.

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