  Skew critical problems occur in continuous and discrete nonholonomic
Lagrangian systems. They are analogues of constrained optimization problems,
where the objective is differentiated in directions given by an apriori
distribution, instead of tangent directions to the constraint. We show
semiglobal existence and uniqueness for nondegenerate skew critical problems,
and show that the solutions of two skew critical problems have the same contact
as the problems themselves. Also, we develop some infrastructure that is
necessary to compute with contact order geometrically, directly on manifolds.
