  Generalizing the canonical symplectization of contact manifolds, we construct
an infinite dimensional non-linear Stiefel manifold of weighted embeddings into
a contact manifold. This space carries a symplectic structure such that the
contact group and the group of reparametrizations act in a Hamiltonian fashion
with equivariant moment maps, respectively, giving rise to a dual pair, called
the EPContact dual pair. Via symplectic reduction, this dual pair provides a
conceptual identification of non-linear Grassmannians of weighted submanifolds
with certain coadjoint orbits of the contact group. Moreover, the EPContact
dual pair gives rise to singular solutions for the geodesic equation on the
group of contact diffeomorphisms. For the projectivized cotangent bundle, the
EPContact dual pair is closely related to the EPDiff dual pair due to Holm and
Marsden, and leads to a geometric description of some coadjoint orbits of the
full diffeomorphism group.
