考虑J2项摄动的Lambert问题状态空间摄动解析近似法  

An Analytical Solution for Lambert Problem with J2 Perturbation Based on State Space Perturbation Method

作　　者：李兆亭 张洪波[1] 郑伟[1] Li Zhaoting;Zhang Hongbo;Zheng Wei(College of Aerospace Science and Engineering,National University of Defense Technology,Changsha 410073,China)

机构地区：[1]国防科技大学空天科学学院,长沙410073

出　　处：《航天控制》2018年第4期52-58,共7页Aerospace Control

摘　　要：针对Lambert转移轨道在考虑J2项摄动时终端位置偏差大的问题,提出了一种基于状态空间摄动法的初始速度修正方法。该方法中初始脉冲速度的主要部分根据二体Lambert变轨原理计算,J2项摄动的修正部分根据状态空间摄动法解析计算。为求得修正量,在当地水平坐标系中建立线性化摄动运动方程,并令线性系统的零输入响应和零状态响应在终端点处相互抵消,从而得到解析解。通过数值仿真验证了该方法的有效性,J2项摄动条件下的终端位置精度能够满足一般的任务要求,但其位置精度受转移时间影响较大。Due to the Lambert problem widely occured in spacecraft transfer orbit design,which make the positional deviation of the Lambert transfer orbit large by considering the J2 perturbation. An initial velocity correction method based on the State Space Perturbation Method is proposed. The main part of the initial maneuver impulse is calculated by solving the two-body Lambert problem,and the modified part of the J2-perturbation is calculated by using the state space perturbation method. In order to obtain the correction velocity,a linearized perturbation equation is established in the local-vertical-local-horizontal coordinate system. The analytic results are obtained by making the zero-input response that is opposite to the zero-state response of the linear system at the terminal point. The validity of this method is verified by numerical simulations. The result is proven that the accuracy of the terminal position under the J2 perturbation can meet general task requirements. But its position accuracy is affected by the transfer time.

关 键 词：状态空间摄动法 Lambert问题 J2项摄动 解析解法 

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]