OPTIMAL CONTROL OF PROPELLANT CONSUMPTION DURING INSERTION OF ROCKET INTO A CIRCLE ORBIT OF THE EARTH

Aleksey G. Vikulov

doi:10.5937/jaes0-28127

Aleksey G. Vikulov Moscow Aviation Institute (National Research University), Department of Space System Engineering, Moscow, Russian Federation

DOI: https://doi.org/10.5937/jaes0-28127

Keywords: ballistics, inverse problems, regularization method, variation principle, Euler equation

Abstract

The problem of launching a rocket into the Earth’s orbit has already been solved using the regularization method in previous studies. But the regularization method remains relevant for application to solving integral equations of the first kind, which determine the components of speed and acceleration. Problem of optimal control of propellant consumption during insertion of a rocket into a circle orbit of the Earth is solved using regularized solutions of integral equations of the first kind which are solutions of corresponding Euler equations on discrete time net. Influence of regularization parameter and some additional parameters on precision of discredited problem is investigated. Calculations are carried out for existing chemical rocket engine and promising plasmic one. Considered algorithm is summed up easily to problem of suborbital flights by setting desired coordinate system and modifying motion equations. Conclusions were drawn about the required speed for the lowest fuel consumption, as well as about the problem for a single-stage rocket. Thus, the development of a plasma rocket engine with an exhaust velocity is more than ten times higher than that of a chemical one.

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