A new method for finding solutions of the nonlinear equilibrium equations for rotational polytropes was proposed, which is based on a self-consistent description of internal region and periphery using the integral form of equations. Dependencies of geometrical parameters, surface form, mass, moment of inertia and integration constants on angular velocity were calculated for indices $n=2.5$ and $n=3$.
Calculations of characteristics of stars with axial rotation in the frame of polytropic model are based on the solution of mechanical equilibrium equation – differential equation of second order in partial derivatives. Different variants of approximate determinations of integration constants are based on traditional in the theory of stellar surface approximation, namely continuity of gravitational potential in the surface vicinity. We proposed a new approach, in which we used simultaneously differential and integral forms of equilibrium equations. This is a closed system and allows us to
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