摘要
给出了在惯性坐标系下两飞行器相对运动动力学方程近似模型的再生核方法。该近似模型适于研究两飞行器做相对运动距离不是很大的圆轨道或近似圆轨道，且控制系统采用陀螺惯性平台的情况，因为此时的近似模型没有解析解，需用数值方法求解。提出的再生核解法是以函数项级数形式表达的，其优点是级数项每增加一项，误差在Sobolev范数意义下单调下降，且该方法易于编程，很适用于在计算机上实施。在数值实验里验证了所提方法的有效性，并显示了再生核解法比常用的数值积分法求解该类方程解的精度高。
This paper represents the reproducing kernel mothod to solve the approximate model of dynamics equations under the inertial coordinates for two aircraft to move relatively. It is suitable for the situation that the approximate model is used to study two aircraft make relative motion in the round orbit or approximate round orbit no longer distance between them, and the control system adopts the top inertia platform, because under this situation, the approximate model hasn＇t analytic solution and has to be solved by the numerical method. The proposed reproducing kernel mothod is expressed in a function progression form, its advantages are whether progression item increases one each time, error in Sobolev norm increases, and this method is easy in programming, is very suitable for implementing on the computer. It is proved validity of the proposed method in the experiment, and shows the precision of solution be higher for reproducing kernel method to solve the equation belong to the same category than a commonly used numerical integration method.
出处
《宇航学报》
EI
CAS
CSCD
北大核心
2006年第B12期145-149,154,共6页
Journal of Astronautics
关键词
再生核方法
空间飞行器
相对运动
动力学方程
近似模型
Reproducing kernel
Space aircraft
Relative motion
Dynamics equation
Approximate model
