基于B平面的火星探测直接转移轨道设计方法

将轨道设计转化为常微分方程两点边值(TPBVP)问题,采用微分修正法求解该边值问题.将B平面概念同时应用于地球和火星,借助B平面与双曲线轨道的几何关系解析地给出了两点边值问题的边界条件的建立方法,理论上说明了火星探测直接转移轨道存在4组解的原因,同时提出了控制探测器到达相对火星双曲线轨道近火点时刻的准确参数表示方法.最终给出仿真算例,将轨道设计结果代入STK,结果合理.

Direct Transfer Trajectory Design for Mars Exploration Using B-plane

The trajectory design problem was transformed into two point boundary value problem(TPBVP) of ordinary differential equation and solved by differential correction.The concept of B-plane was used near earth and Mars.The boundary condition of the TPBVP can be analytically determined by the geometrical characteristics between B-plane and its associated hyperbolic orbit,and the reason that four kinds of trajectories can be obtained was explained.An accurate mathematical formulation describing the closest approach time to Mars was also proposed.An illustrative example was presented and the results were coincided with satellite tool kit.