### Method for optimizing the flight path to the final orbit with partially specified elements

**Published:**11.09.2020

**Authors:** Paing S.T.O.

**Published in issue: **#9(105)/2020

**DOI: **10.18698/2308-6033-2020-9-2017

**Category:** Aviation and Rocket-Space Engineering | **Chapter:** Aircraft Dynamics, Ballistics, Motion Control

The paper focuses on the problem of optimizing the interorbital flight of a spacecraft (SC) at a fixed time interval from a given initial orbit to a final orbit with partially given elements in the Earth’s gravitational field. The optimization goal is to calculate the program for controlling the spacecraft reactive acceleration vector, which ensures such a flight with the minimum relative velocity. The magnitude of the reactive acceleration is assumed to be constant, the reactive acceleration vector orientation program and the program of its on-off are optimized. To solve the problem of trajectory optimization, an approach based on Pontryagin’s maximum principle is proposed. Using the maximum principle, the problem of optimizing the interorbital flight of a spacecraft with a limited acceleration engine is reduced to a two-point boundary value problem. To optimize the free elements of the finite orbit, transversality conditions are used and these conditions are met when solving the boundary value problem. A method has been developed to optimize the trajectory of a transfer to the final orbit with a free value of the true anomaly, longitude of the ascending node and the pericenter argument.

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