J_2项摄动条件下线性化的编队卫星动力学方程  

Linearized Formation Flight Dynamics Model under J_2 Perturbation

作　　者：杏建军[1] 时伟[1] 蒋炳炎[1] 

机构地区：[1]中南大学航空航天学院,长沙410083

出　　处：《宇航学报》2013年第5期605-610,共6页Journal of Astronautics

基　　金：中国博士后科学基金(20080440217;200902666)

摘　　要：考虑J2项摄动力对参考卫星轨道的绝对影响和对伴随卫星轨道的相对影响,应用拉格朗日方法,在笛卡尔坐标系下,给出了一组考虑J2项摄动的线性化的编队卫星相对动力学方程。该方程考虑了J2项摄动力带来的相对运动平面内外的耦合和短周期项的影响,有效地提高了相对动力学模型的精度。仿真结果表明,该方程组可有效地描述J2项摄动条件下编队卫星的相对运动,其误差只有二体非线性模型的10%,利用其设计的水平圆编队半径的相对误差不超过1%,并且由于是线性化的微分方程描述,可方便地应用到编队卫星导航、制导与控制系统的设计中。A linear model including J2 perturbation in the Cartesian coordinates is presented for spacecraft formation flight.The Lagrange method is used to obtain this model by including the absolute effect on the reference orbit and the relative effect on the relative motion of the formation satellites under the J2 perturbation.This model accounts for the short-period perturbation of the orbital radius of the reference satellite and the angular velocities of the chief-fixed rotating reference frame,which also does not neglect the coupling terms between the out-of-plane and in-plane equations,thus leading to the improvement of accuracy.A numerical simulation illustrates that the relative trajectory error of this model is only 10% with respect to the nonlinear two body propagator model,and the relative radius error of the projected circular formation is less than 1%.At the same time,the model is linear state space form that is convenient to design the guidance,navigation and control system in formation flight missions.

关 键 词：卫星编队 J2项摄动 动力学方程 笛卡尔坐标 

分 类 号：V412.41[航空宇航科学与技术—航空宇航推进理论与工程]