  We take advantage of different generalizations of the tangent manifold to the
context of graded manifolds, together with the notion of super section along a
morphism of graded manifolds, to obtain intrinsic definitions of the main
objects in supermechanics such as, the vertical endomorphism, the canonical and
the Cartan's graded forms, the total time derivative operator and the
super--Legendre transformation. In this way, we obtain a correspondence between
the Lagrangian and the Hamiltonian formulations of supermechanics.
