Radial kinetic nonholonomic trajectories are Riemannian geodesics!

2020/10/23 by Alexandre Anahory Simoes, Juan Carlos Marrero, Simoes, Alexandre Anahory +3 · 1 citation
Engineering · Physics and Astronomy · #37J60 #53B20 #53C21 #70F25 (Secondary) #70G45 (Primary) #Advanced Differential Geometry Research #Control and Dynamics of Mobile Robots #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.2010.12444

openalex publication_date 2020/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Nonholonomic mechanics describes the motion of systems constrained by nonintegrable constraints. One of its most remarkable properties is that the derivation of the nonholonomic equations is not variational in nature. However, in this paper, we prove (Theorem 1.1) that for kinetic nonholonomic systems, the solutions starting from a fixed point q are true geodesics for a family of Riemannian metrics on the image submanifold \mathcal M^nh_q of the nonholonomic exponential map. This implies a surprising result: the kinetic nonholonomic trajectories with starting point q, for sufficiently small times, minimize length in \mathcal M^nh_q!

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