Strained coordinate methods in rotating stars

It was shown in a previous paper (Smith, 1976) that the method of strained coordinates may be usefully employed in the determination of the structure of rotating polytropes. In the present work this idea is extended to Main-Sequence stars with conservative centrifugal fields. The structure variables, pressure, density and temperature are considered pure functions of an auxiliary coordinates (the strained coordinate) and the governing equations written in a form that closely resembles the structure equations for spherical stars but with correction factors that are functions ofs. A systematic, order-by-order derivation of these factors is outlined and applied in detail to a Cowling-model star in uniform rotation. The technique can be extended beyond first order and external boundary conditions are applied, as they should be, at the true surface of the star. Roche approximations are not needed.