Abstract—

The study proposes a regular method that allows one to find (one or more) solutions of a multi-extreme problem for optimizing the transfer of a spacecraft, equipped with a perfectly controlled electro-jet propulsion system, in a central gravitational field. The method consists of three main stages. In the first stage, using an algorithm based on the Bellman optimality principle, for various values of angular range, the composite transporting trajectories are generated in an impulse formulation. In the second stage, in the vicinity of these trajectories, the first-approximation trajectories with continuous control are formed using the local variation method. At the third stage, the latter trajectories are used to find an accurate solution of a nonlinear boundary value problem. Then, the results are analyzed to determine the optimum. The numerical example of using this method to construct optimal trajectories of spacecraft transfer from Earth to the Apophis asteroid is presented.

中文翻译：

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一种利用电子喷气推进系统推力优化航天器弹道的多极端问题的方法

摘要-

这项研究提出了一种常规方法，该方法可以让人们找到（一个或多个）多重极端问题的解决方案，以优化在中央引力场中配备了完善控制的电喷推进系统的航天器的传递。该方法包括三个主要阶段。在第一阶段，使用基于Bellman最优性原理的算法，对于各种角度范围值，以脉冲形式生成复合运输轨迹。在第二阶段中，在这些轨迹附近，使用局部变化法形成具有连续控制的第一近似轨迹。在第三阶段，使用后者的轨迹找到非线性边值问题的精确解。然后，分析结果以确定最佳值。