  In the present article the geometry of semi-Riemannian manifolds with
nonholonomic constraints is studied. These manifolds can be considered as
analogues to the sub-Riemannian manifolds, where the positively definite metric
is substituted by a nondegenerate metric. To study properties of the
exponential map the Christoffel symbols and other differential operators were
introduced. We study solutions of the Hamiltonian system and their projections
into the underlying manifold. The explicit formulae were found for a specific
example of a semi-Riemannian manifold with nonholonomic constraints.

Differential Geometry;Optimization and Control