  In the framework of finite order variational sequences a new class of
Lagrangians arises, namely, \emph{special} Lagrangians. These Lagrangians are
the horizontalization of forms on a jet space of lower order. We describe their
properties together with properties of related objects, such as
Poincar\'e--Cartan and Euler--Lagrange forms, momenta and momenta of generating
forms, a new geometric object arising in variational sequences. Finally, we
provide a simple but important example of special Lagrangian, namely the
Hilbert--Einstein Lagrangian.
