On a geometric framework for Lagrangian supermechanics
  We re-examine classical mechanics with both commuting and anticommuting degrees of freedom. We do this by defining the phase dynamics of a general Lagrangian system as an implicit differential equation in the spirit of Tulczyjew. Rather than parametrising our basic degrees of freedom by a specified Grassmann algebra, we use arbitrary supermanifolds by following the categorical approach to supermanifolds. 
Andrew James Bruce, Katarzyna Grabowska and Giovanni Moreno
math-ph hep-th math.DG math.MP math.QA