基于有限Fourier级数的航天器转移轨迹设计

针对航天器小推力转移轨迹的初始设计问题，利用基于三阶Fourier级数的设计方法实现了航天器小推力的多圈转移。同时，基于有限Fourier级数的形状法，对具有多个约束条件的小推力多圈转移轨迹进行了优化设计。选取了共面同轴同偏心率的初始和末端轨道位置，对所提出的方法进行了仿真验证。结果表明：与改进逆五阶多项式形状法相比，所提出的方法虽然增加了转移时间，但当转移圈数为5圈、有限Fourier级数的项数为10时，可减少将近75%的转移速度增量，同时大大减小了所需的最大推力加速度的值。

Design of Spacecraft Transfer Trajectory based on Finite Fourier Series

In this paper, for the initial design of spacecraft transfer trajectory via small thrust, a third-order Fourier series design method is proposed to realize multi-turn transfer of spacecraft via small thrust. Based on the shape-based method of finite Fourier series, the trajectory of spacecraft via small thrust with multiple constraints is optimized. The initial and terminal positions in the two-point boundary value problem are selected from coplanar, coaxial and same eccentric orbits, then the proposed method is verified by simulation. The results show that the proposed method can decrease nearly 75% of velocity increase and greatly reduce the needed value of maximum thrust compared with the modified fifth-order inverse polynomial shape-based method when spacecraft transfer 5 turns and the finite Fourier series has 10 terms.