# mechanical equilibrium equation

## The generalized polytropic model for the Sun-like stars

The Eddington method based on simultaneous consideration of gas and light pressures with a homogeneous сhemical composition of stellar matter was generalized for the case of model with a spatially inhomogeneous chemical composition.  As a result, it was obtained the equation of state, which is expressed by a generalized polytrope with index $n=3$.  As an example, it was solved the equilibrium equation for the Sun both using the standard polytropic equation of state and generalized polytrope.  The coordinate dependence of the Sun characteristics was calculated within two

## White dwarfs with rapid rotation

A new analytical approach for calculation of white dwarfs characteristics that accounts for two important competing factors — axial rotation and Coulomb interparticle interactions, is proposed.  The feature of our approach is simultaneous usage of differential and integral forms of equilibrium equation.  In dimensionless form the differential equilibrium equation is strongly nonlinear inhomogeneous equation of the second order in partial derivatives with two dimensionless parameters — the relativistic parameter in stellar center $x_0$ and dimensionless angular velocity

## Method of integral equations in the polytropic theory of stars with axial rotation. II. Polytropes with indices $n>1$

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 $n=3$.

## Method of integral equations in the polytropic theory of stars with axial rotation. I. Polytropes n=0 and n=1

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

## 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