Lunar frozen orbits, characterized by fixed eccentricity and argument of perigee on average, have been previously studied using different dynamical models. In this work, frozen orbits about the Moon are investigated on the basis of an averaged Hamiltonian. The gravitational field of the Moon is considered up to the seven zonal harmonic plus the third body perturbation (Earth). The third body is assumed to move in an elliptic inclined orbit. The averaging procedure is performed through Lie transformation method. We used the eccentricity-inclination diagrams to obtain a deep insight about the evolution of frozen orbits. For the reduced system, we found two frozen solutions which correspond to argument of perigee $\omega =\frac{\pi }{2},\frac{3\pi }{2}$. Moreover, we studied the evolution of the eccentricity and inclination as a function of time. The results showed that, for moderate altitude orbits, the eccentricity oscillates with small amplitudes around its initial value, while the inclination almost remains constant. In higher altitudes case, we observed that variations in eccentricity and inclination are larger than the moderate ones. The present dynamical model gives acceptable results for low initial eccentricity and inclination.

以前曾使用不同的动力学模型研究过以固定偏心率和近地点为论据为特征的月球冻结轨道。在这项工作中，根据平均哈密顿量对绕月球的冰冻轨道进行了研究。月球的引力场被认为不超过七个纬向谐波加上第三次人体扰动（地球）。假定第三物体在椭圆形倾斜轨道上运动。平均过程通过李变换方法执行。我们使用偏心率-倾角图获得了关于冻结轨道演变的深刻见解。对于简化系统，我们发现了两个冻结的解，它们对应于近地点的论点$\omega =\frac{\pi }{2}，\frac{3\pi }{2}$。此外，我们研究了随时间变化的偏心率和倾斜度的变化。结果表明，对于中等高度的轨道，偏心率在其初始值附近以小幅度振荡，而倾斜度几乎保持恒定。在较高海拔的情况下，我们观察到偏心率和倾斜度的变化要比中度变化大。对于低初始偏心率和倾斜度，本动力学模型给出了可接受的结果。