Main Catalog Aviation and Rocket-Space Engineering Aircraft Dynamics, Ballistics, Motion Control

Optimization of the spacecraft launch into orbit

Authors: Gorokhov I.E.
Published in issue: #7(48)/2020
DOI: 10.18698/2541-8009-2020-7-628
Category: Aviation and Rocket-Space Engineering \| Chapter: Aircraft Dynamics, Ballistics, Motion Control
Keywords: optimal control, spacecraft, launch into orbit, pitch angle, boundary value problem, geostationary orbit, Pontryagin’s maximum method, system of differential equations, optimality criterion, launch vehicle
Published: 03.09.2020

A method of optimal launching of a spacecraft into a geostationary orbit is considered, which allows minimizing resource consumption. A mathematical model of the movement of the launch vehicle center of mass is presented. To search for the optimal control, the Pontryagin’s maximum method, dynamic programming method and method based on small variation of parameters. A method of searching for optimal control by varying a parameter is chosen. The following numerical methods for solving the boundary value problem have been studied: Newton’s method and its modifications; shooting method; finite difference method. Using the built-in MATLAB functions, the control law for the pitch angle and the trajectory of the launch vehicle in the equatorial plane is obtained. The simulation of the spacecraft motion using the classical fourth-order Runge-Kutta method with a constant integration step is carried out.

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