On the exponential mapping of geodesics in sub-Riemannian geometry

The equations of admissible geodesics for a nonholonomic distribution on Riemannian manifold are written in the mixed bundle. The differential of the exponential mapping for a nonholonomic distribution with the cyclicity condition for vertical coordinates is calculated. This differential is non-degenerate if the distribution is strongly bracket generating. The equations of admissible geodesics on 3-dimensional Lie groups are studied.