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 orderordinary 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 viceversa, so we have a sequence of supersprays via nonlinear connections associated withthem. using this idea and under the conditions on lagrangian superfunctions, we willfind a nonlinear connection n 1 such that its superspray determines the above nonlinear connection n.