为什么发射轨迹向下终止

摘要：

分析了某发射装置末级最佳推力分布的求解问题。假设发动机连续推进，遵循线性或双层参数轮廓，直到到达目标共面轨道。最小燃料问题的分析解决使用最大值原理。推力方向的闭环解的推导和最后一点被发现必然是在一个近地点注入的情况下，向下到达的近地点。最优控制问题归结为一个只有推力剖面参数为未知数的非线性问题。以地球静止转移轨道为目标的应用实例说明了该方法的求解过程。

英文摘要：

The problem of finding the optimal thrust profile of a launcher upper stage is analyzed. The engine is assumed to be continuously thrusting, following either a linear or a bilevel parametric profile, until reaching the targeted coplanar orbit. The minimum-fuel problem is analytically solved using the maximum principle. A closed-loop solution for the thrust direction is derived and the final point is found to be necessarily at an apside, reached downwards in the case of a perigee injection. The optimal control problem reduces to a nonlinear problem with only the thrust profile parameters as unknowns. An application case targeting a geostationary transfer orbit illustrates the solution method.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。