Controllability Analysis of Motion of Artificial Satellite Under the Effect of Oblateness of the Earth

TL;DR

This paper investigates the controllability of an artificial satellite affected by Earth's oblateness using linearized equations, Kalman test, and various thruster configurations, demonstrating controllability under specific conditions.

Contribution

The study applies Kalman controllability test to satellite motion with Earth's oblateness and analyzes multiple thruster configurations for controllability.

Findings

System controllable with thrusters in r, θ, or z directions.

Linearized equations and Kalman test confirm controllability.

Controller u derived and trajectories plotted to demonstrate control.

Abstract

In this article we have studied the controllability of artificial satellite under the effect of zonal harmonic $J_2$ in cylindrical polar coordinates systems. Seven different cases of thrusters in various directions have been analyzed and it is found that the system is controllable if we apply thrusters in either $r$, $\theta$ and $z$ or $\theta$ and $z$ direction. The equations governing motion of satellite have been linearized and Kalman controllability test is applied to check the controllability of the system. We have also derived controller $u$ for the linearized system. The trajectory of the system have been plotted to show the controllability of the system.