HAMILTONIAN VERSUS LAGRANGIAN FORMULATIONS OF SUPERMECHANICS

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 def initions of the main objects in supermechanics such as, the vertical e ndomorphism, the canonical and the Cartan's graded forms, the total ti me derivative operator and the super-legendre transformation. In this way, we obtain a correspondence between the Lagrangian and the Hamilto nian formulations of supermechanics.