INTRODUCING A NONLINEAR CONNECTION IN A LAGRANGIAN SUPERMECHANICAL SYSTEM

In this paper, we study the concept of a Lagrangian supermechanical system. The dynamical system of a Lagrangian supermechanical system defined by a second order ordinary differential equation which introduce a superspray S as a solution of the Euler- Lagrange equation. There is a nonlinear connection N, induced by this superspray. Since every superspray on a supermanifold determines a nonlinear connections and vice versa, so we have a sequence of supersprays via nonlinear connections associated with them. Using this idea and under the conditions on Lagrangian superfunctions, we will find a nonlinear connection N 1 such that its superspray determines the above nonlinear connection N.