地球扁率影响下人造卫星运动的可控性分析
Controllability Analysis of Motion of Artificial Satellite Under the Effect of Oblateness of the Earth
摘要：
本文研究了柱极坐标系统中带谐$J_2$作用下的人造卫星的可控性。分析了推力器在不同方向上的七种不同情况，发现在$r$、$θ$和$z$或$θ$和$z$两个方向上施加推力器，系统都是可控的。对卫星运动方程进行线性化处理，并利用卡尔曼能控性检验检验系统的能控性。我们还推导出控制器$u$的线性化系统。绘制了系统的运动轨迹，证明了系统的可控性。
英文摘要：
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 $r$, $θ$ and $z$ or $θ$ 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.
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