2002/06/24 by Craig Calcaterra, Calcaterra, Craig, Axel Boldt +5 · 1 citation
Engineering · Mathematics · #34G99 (Primary) 54E45 (Secondary) #37C10 #Control and Dynamics of Mobile Robots #Dynamical Systems (math.DS) #FOS: Mathematics #Metric Geometry (math.MG) #math.DS #math.MG #msc:34G99 #msc:37C10 #msc:54E45
paper · pdf · doi:10.48550/arxiv.math/0206253
31 pages, 2 figures
arxiv created 2002/06/24 · openalex publication_date 2002/06/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Coordinate systems are defined on general metric spaces with the purpose of generalizing vector fields on a manifold. Conversion formulae are available between metric and Cartesian coordinates on a Hilbert space. Nagumo's Invariance Theorem is invoked to prove the analogue of the classical Cauchy-Lipschitz Theorem for vector fields on a locally compact coordinatized space. A metric space version of Nagumo's Theorem is one consequence. Examples are given throughout.