The self-consistent description of stellar equilibrium with axial rotation

New method for the description of mechanical equilibrium of stellar structure with axial rotation was proposed.  The self-consistent calculation is based on simultaneous use of differential and integral forms of mechanical equilibrium equation, which allows us to correctly determine the integration constants.  In the frame of polytropic model with indexes n=0 and 1 were first obtained the analytical solutions, for n=2 and 3 numerically.  The geometrical parameters of stellar surface as well as mass, volume and moment of inertia  were calculated as the functions of angular velocity.  It was found the maximal value of angular velocity in which the stability is disturbed.  Obtained results improve the results of E. Milne, S. Chandrasekhar and R. James, obtained with help of the approximate numerical integration of mechanical equilibrium  equation.

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