卫星编队相对动力学方程稳定性分析

Stability Analysis of Spacecraft Formation Relative Dynamics Equation

编队飞行是多颗卫星在共同控制律下动力学状态的耦合。稳定性是卫星编队动力学状态耦合分析的重要内容之一。以主星运动的真近点角为参数,在不考虑摄动的情况下,建立了卫星编队相对动力学方程。根据李亚普诺夫稳定性定理,分析了相对动力学方程中非线性项对卫星编队一阶近似方程的稳定性影响。得出了非线性项对一阶近似的稳定性影响与编队卫星的主星偏心率有关的结论。

Formation flying is a set of more than one spacecraft whose dynamic states are couples through a common control law. In this paper, true anomaly of the chief satellite was taken as basic parameter, in unperturbed situation, formation flying relative dynamic equation was modeled. Then according to Lyapunov stability theory, stability of nonlinear term to 1 st order approximation of the relative dynamic equation was analyzed. A conclusion was drawn that stability of nonlinear term to 1 st order approximation was related to eccentricity of chief satellite.