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arXiv · 1706.01044

Why do launch trajectories end downwards

Max Cerf
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Abstract

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.

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Max Cerf. 2017-06-04. Why do launch trajectories end downwards. https://arxiv.org/abs/1706.01044

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