中文摘要：

为提高行星际小推力转移轨道初始设计精度，提出了基于N次逆多项式逼近的半解析Lambert算法，并基于该算法发展了一种转移轨道初始设计方法。首先，采用N次逆多项式近似小推力轨道形状，应用推力方向假设和位置速度边界条件推导出部分系数及推力大小解析式。接着，分析了飞行时间约束和轨道动力学约束下解的存存性，并给出了关键系数的可行域。然后，利用探测器质量消耗方程建立了Lambert问题求解模型并加以解决。最后，基于所提Lambert算法，通过对连续推力约束进行降维，提出一种求解多圈非固定时间的行星际小推力转移轨道初始设计方法。分别以固定和非固定时间转移任务为例对所提Lambert算法和初始轨道设计方法进行了数学仿真，数值结果表明：相比传统6阶方法，所提Lambert算法在目标轨道半长轴为5AU时可减少速度增量需求36．63％；所提初始设计方法与最优化方法设计结果接近，可为转移轨道的精确设计提供可行的设计初值。

英文摘要：

In order to improve the precision of primary design for an interplanetary low-thrust transfer trajectory, a semi-analytical Lambert algorithm based on the N-degree inverse polynomial approach is proposed, and a primary design method is developed accordingly. First, the N-degree inverse polynomial is used to approximate the low thrust trajectory, and the partial coefficients as well as the analytical solution of the thrust are derived with the thrust direction assumption and trajectory boundary conditions. Next, the existent feasibility of the Lambert solution is analyzed and the feasible region of the key coefficient is presented taking into consideration the fly time and orbit dynamical constraints. Then, a computation model for the Lambert problem is established using the spacecraft mass equation. Finally, based on the Lambert algorithm, a primary design approach for a multi-revolution, free-time transfer trajectory is presented through reducing the dimensions of the thrust constraints. The proposed Lambert algorithm and primary design method are validated by computer simulations. The numerical results demonstrate that, for a target orbit with 5 AU semi-major axis, the Lambert algorithm can reduce the velocity increment by 36.63% as compared with the traditional six order algorithm. The primary design solution, which is very close to that of the optimal method, can provide a feasible guess for an accurate design problem.