带脉冲的三维引力辅助变轨研究  

POWERED GRAVITY ASSIST IN THREE DIMENSIONS

作　　者：贾建华[1] 吕敬[1] 王琪[1] 

机构地区：[1]北京航空航天大学航空科学与工程学院,北京100191

出　　处：《力学学报》2016年第2期437-446,共10页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金资助项目(11372018)

摘　　要：在引力辅助过程中施加脉冲可以有效地改善变轨效果.目前只能对施加小脉冲的情况进行近似计算,当脉冲大于近拱点速度的1%时无法进行分析.针对这一问题,提出了一种解析分析方法,可以计算施加任意大小和方向脉冲的三维引力辅助变轨.基于二体问题,建立了带任意脉冲的三维引力辅助模型,采用8个相互独立的参数对模型进行描述,其中5个参数表征三维引力辅助、一个参数表征脉冲的大小、两个参数表征脉冲的方向;建立了一组坐标系,可以方便地对轨道进行描述;以施加脉冲为界,将轨道划分为前后两段,分别进行公式推导;应用双曲线轨道动力学与坐标变换等技术方法,可以将飞行器的位置矢量和速度矢量表示为上述8个参数的解析公式,进而可以求出变轨导致的速度、能量和轨道倾角的变化量.通过与基于圆型限制性三体问题的数值仿真结果进行对比,验证公式的有效性.应用导出的解析公式分析了施加脉冲的大小和方向对飞行器能量和轨道倾角的影响,并给出了相应规律.结果表明:以最大能量改变为优化目标,施加脉冲的最优方向往往并不是该点速度方向;轨道倾角受到脉冲方向的影响显著.Applying an impulsive thrust during a close encounter with a celestial body can significantly improve the efficiency of the swing-by maneuver. In the existing literature, no analysis can be carried out when the impulse velocities are bigger than 1% of the orbital velocity of the spacecraft. To solve this problem, powered gravity assist is studied applying an arbitrary impulse with any magnitude and direction. The three-dimensional powered gravity assist maneuver based on the patched-conics approximation can be identified by eight independent parameters, in which five specify the three-dimensional gravity assist and the other three specify the magnitude and the direction of the impulse. Multiple reference frames are established to describe the trajectories before and after the impulse. Using the method of coordinate transformation and hyperbolic orbit dynamics, a set of new analytical equations are derived, including the variation in velocity, angular momentum, energy and inclination of the spacecraft due to the maneuver as a function of the eight parameters. These equations developed here are verified by numerical integrations, using the circular restricted threebody problem. Finally, the influences of the parameters on the orbit of spacecraft are discussed based on the above equations, and some conclusions about the optimal direction to apply the impulse are given. The results show that theoptimal direction of the impulse is not parallel to the velocity of the spacecraft, and the orbital inclination is significantly influenced by the direction of the impulse.

关 键 词：三维引力辅助 脉冲 变轨 二体问题 解析公式 最优方向 

分 类 号：V41[航空宇航科学与技术—航空宇航推进理论与工程]