受摄三体问题研究

圆型限制性三体问题模型忽略了摄动因素的影响,在很多情况下不能足够准确地描述三体系统的动力学性质。本文研究了考虑摄动影响的三体问题的动力学性质及其轨道设计。首先分析了运行在平动点附近的卫星所受的主要摄动因素;然后从系统在惯性坐标系中的动力学方程出发,推导了会合坐标系中考虑偏心率、第四体引力以及太阳光压摄动影响的一般动力学方程;最后使用两层微分修正方法将圆型限制性三体问题模型下设计的轨道转换到受摄三体问题模型下。

Research on the Perturbed Three-body Problem

Since the circular restricted three-body problem model ignores the effect of perturbations,it can not accurately describe the dynamic characters of the three-body system.The dynamic characters and orbit design strategy of the perturbed three-body problem model was studied.Firstly,main perturbations of libration point missions were analyzed,and then the general dynamic equation of the perturbed three-body problem in the synodic frame was concluded from the dynamic equations in the inertial frame considering the effects of the eccentricity,the gravity of the fourth body and the solar radiation pressure.Finally,the two level differential corrections method was proposed to transform the orbit designed under the circular restricted three-body problem model into the perturbed three-body problem model.