针对冲量方向与追踪器速度方向相同的正切轨道问题,用线性相对运动方程研究了正切于初始轨道和正切于目标轨道的共面轨道拦截和轨道交会问题。得到初始和终端时刻的相对速度向量的解析表达式,定义了两个关于目标真近点角的单变量函数,于是正切拦截和正切交会问题等价于这两个函数分别等于零,最后用割线法求解这两个函数的数值解。根据能量最优要求,考虑初始漂移段,分析了一个周期内的最佳初始正切冲量点。仿真结果校验了本文提出的方法。
For the tangent orbit problem with impulse and chaser' s velocity in the same direction, by using the linear relative motion equations the coplanar orbit interception and orbit rendezvous problems tangent to the initial orbit and the final orbit are studied. The analytical expressions for relative velocities at initial and final times are obtained, and then two functions only about the final true anomaly are defined. These two functions are equal to zero in the orbit interception and the orbit rendezvous problems, respectively. Then the secant method is used to obtain the numerical solutions. For the minimum-cost demand, the initial coasting time is considered, and the optimal first tangent-impulse time is analyzed. Simulation results are used to verify the proposed method.