ИСТИНА

The admissible velocities of a drifted sub-Riemannian control system on a three-dimensional manifold form, by definition, an ellipse lying in an affine plane of the tangent space. We classify generic points of such systems into two types: contactly hyperbolic and contactly elliptic. In particular, all points of the control system naturally defined by a contact sub-Riemannian structure are contactly elliptic. This classification is a reformulation of the Arnold two types of contact structures in a neighborhood of a cone. We describe the front and its singularities of a contactly hyperbolic point for small times, and formulate a conjecture asserting that the front of a contactly elliptic point is the sub-Riemannian sphere, investigated by A.A.Agrachev in 1996.