GEOMETRIC FORMULATION OF HIGHER-ORDER LAGRANGIAN SYSTEMS IN SUPERMECHANICS

Using supervector fields along a morphism of graded manifolds, we stud y both the geometry of the tangent supermanifolds of an arbitrary orde r and kth-order ordinary differential superequations, in order to deve lop the higher-order Lagrangian formalism of supermechanics. In partic ular, we obtain, in this formalism, a generalization of Noether's theo rem and its converse.