Radial kinetic nonholonomic trajectories are Riemannian geodesics!

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 ${\mathcal{M}}_q^{nh}$ 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 ${\mathcal{M}}_q^{nh}$!

arXiv comment30 pages

References in corpus (5)

• Nonholonomic LR systems as Generalized Chaplygin systems with an Invariant Measure and Geodesic Flows on Homogeneous Spaces
• On the Integration Theory of Equations of Nonholonomic Mechanics
• Conservation of `moving' energy in nonholonomic systems with affine constraints and integrability of spheres on rotating surfaces
• Gauge momenta as Casimir functions of nonholonomic systems
• Jacobi fields in nonholonomic mechanics

Cited by in corpus (1)

• Contact bundle formulation of nonholonomic Maupertuis-Jacobi principle and a length minimizing property of nonholonomic dynamics