  We demonstrate how the novel approach to the local geometry of structures of
nonholonomic nature, originated by Andrei Agrachev, works in the following two
situations: rank 2 distributions of maximal class in R^n with non-zero
generalized Wilczynski invariants and rank 2 distributions of maximal class in
R^n with additional structures such as affine control system with one input
spanning these distributions, sub-(pseudo)Riemannian structures etc. The common
feature of these two situations is that each abnormal extremal (of the
underlying rank 2 distribution) possesses a distinguished parametrization. This
fact allows one to construct the canonical frame on a (2n-3)-dimensional bundle
in both situations for arbitrary n greater than 4. The moduli spaces of the
most symmetric models for both situations are described as well. The relation
of our results to the divergence equivalence of Lagrangians of higher order is
given
