  In this paper we analyse the optimality of broken Pontryagin extremal for an
n-dimensional affine control system with a control parameter, taking values in
a k- dimensional closed ball. We prove the optimality of broken normal
extremals when n = 3 and the controllable vector fields form a contact
distribution, and when the Lie algebra of the controllable fields is locally
orthogonal to the singular locus and the drift does not belong to it. Moreover,
if k = 2, we show the optimality of any broken extremal even abnormal when the
controllable fields do not form a contact distribution in the point of
singularity.
