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See detailOn a geometric framework for Lagrangian supermechanics
Bruce, Andrew UL; Grabowska, Katarzyna; Moreno, Giovanni

in Journal of Geometric Mechanics (2017), 9(4), 411-437

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 ... [more ▼]

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. [less ▲]

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