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Nonholonomic mechanics describes the motion of systems constrained bynonintegrable constraints. One of its most remarkable properties is that thederivation 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 fora family of Riemannian metrics on the image submanifold ${\mathcal M}^{nh}_q$of the nonholonomic exponential map. This implies a surprising result: thekinetic nonholonomic trajectories with starting point $q$, for sufficientlysmall times, minimize length in ${\mathcal M}^{nh}_q$!

Radial kinetic nonholonomic trajectories are Riemannian geodesics!