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The paper considers Euler-Poisson equations which govern the steady state ofa self gravitating, rotating, axi-symmetric fluid under the additionalassumption that it is incompressible and stratified. In this setting we showthat the original system of six nonlinear partial differential equations can bereduced to two equations, one for the mass density and the other forgravitational field. This reduction is carried out in cylindrical coordinates.As a result we are able to derive also expressions for the pressure as afunction of the density. The resulting equations are then solved analytically.These analytic solutions are used then to determine the shape of the rotatingstar (or interstellar cloud) by applying the boundary condition that thepressure is zero at the boundary.

Reduction of Stratified Axi-Symmetric Euler-Poisson Equations Under Symmetry