The source of this idea lies in mechanics are phase spaces (cotangent bundles to configurational manifolds) on which there always exists the canonical symplectic structure. The source of contact structures are manifolds of contact elements of configuration spaces. A contact element to an n-dimensional smooth manifold at a given point is a (n-1)-dimensional tangent plane to the manifold at this point (or a (n-1)-dimensional linear subspace of an n-dimensional tangent space at this pont). The set of all contact elements of an n-dimensional manifold has a natural smooth manifold structure of dimension (2n-1). (It can also be described as an associated bundle - it is a projective space bundle associated to the tangent bundle as vector bundle.)

It turns out that on this manifold with odd dimension there is an outstanding additional structure, now called a contact structure. Formally it is given by the data of a differential form α of degree 1, such that the wedge product of α with n−1 copies of dα makes up a non-vanishing (anywhere) 2n−1-form Ω.

The manifold of contact elements of an n-dimensional Riemannian manifold is strictly related to the (2n-1)-dimensional manifold of unit tangent vectors to this manifold, or with (2n-1)-dimensional isoenergetic manifold of a material point moving inertially on the Riemannian manifold. On the other hand, contact structures on these (2n-1)-dimensional manifolds are connected to the symplectic structure in (2n)-dimensional phase space of this point (or in the cotangent bundle of the n-dimensional Riemannian manifold).