本文将多方球内部的引力势能与自转带来的离心势能一并考虑进流体静力学平衡方程，并利用多方关系得到一个自转情形下可以描述恒星内部结构的微分方程，然后考虑自转较慢的情况，利用微扰展开和分离变量的方法进行近似求解，最后讨论自转多方球模型的外边界、内部密度分布及质量半径关系.

Polytrope is often used to describe the internal structure of gaseous stars. For a stationary polytropes, the Lane-Emden equation can be obtained bycombing the hydrostatic equilibrium equation with the polytropic equation, and the internal structure of the star can be determined approximately by solving the equation. But for the more general cases, the star is in rotation. Hence the influence of rotation on the outer boundary and inner structure of the polytrope model is particularly important. This paper firstly substitutes the rotation into the hydrostatic equilibrium equation and combines the polytropic equation to obtain a differential equation that can describe the internal structure of the star in the case of rotation, and then considers the case of slow rotation, and uses the method of perturbation expansion and separation of variables to obtain a approximated solution. Finally, the outer boundary, internal density distribution and the relationship of mass and radius of the rotation polytrope are discussed through the approximated solution.