Body of revolution phi flip matrix and BOR-PATCH system matrix optimization

A new phi flip unit matrix is introduced into the body of revolution (BOR) system matrix theory which aides in the development of negative mode expressions for the impedance, admittance, voltage, current, and row matrices. A demonstration of the phi hip matrix provides a succinct proof of existing results for scattered fields using positive modes. The BOR-PATCH system matrix equation and its solution are then presented using the phi flip matrix to optimize the partition solution. It is shown that the Z_effective matrix is symmetric and may be computed using positive modes and that the row R_effective measurement matrix may be obtained directly from the transpose of the V_effective excitation column matrix. For this work, the entire polarization scattering matrix is the goal since the optimizations introduced operate better at this level of formulation