Hamilton-Jacobi mechanics from pseudo-supersymmetry

For a general mechanical system, it is shown that each solution of the Hamilton Jacobi equation defines an N=2 pseudo-supersymmetric extension of the system, such that the usual relation of the momenta to Hamilton's principal function is the 'BPS' condition for preservation of 1/2 pseudo-supersymmetry. The examples of the relativistic and non-relativistic particle, in a general potential, are worked through in detail and used to discuss the relation to cosmology and to supersymmetric quantum mechanics.