小推力限制性三体系统下稳定平动点附近的高阶解  

High-order solutions around the stable libration points in the low-thrust restricted three-body system

作　　者：雷汉伦[1] 徐波[1] 

机构地区：[1]南京大学天文与空间科学学院,南京210093

出　　处：《中国科学：技术科学》2015年第11期1207-1217,共11页Scientia Sinica(Technologica)

基　　金：国家重点基础研究发展计划(批准号:2013CB834103);国家高技术研究发展计划(批准号:2012AA121602);国家自然科学基金(批准号:11078001);中央高校基本科研业务费(批准号:CXZZ13_0042)资助项目

摘　　要：小推力可使得限制性三体系统下的非平衡点转变为人工平动点,处于该点的航天器在会合系下与两主天体相对静止.人工平动点丰富了经典限制性三体系统的平动点轨道资源,可较大程度地满足深空任务对平动点轨道的需求,从而使得任务设计更加灵活.稳定人工平动点附近的轨道有较好的稳定性,以此为任务轨道只需少许的燃料消耗即可实现轨道保持.考虑到稳定人工平动点的动力学性质,将其附近的拟周期轨道展开为长周期振幅、短周期振幅以及垂直周期振幅的级数解形式,构造了任意高阶的级数解.构造的级数解可较好地近似人工平动点附近的运动,并且表征这些轨道的参数有助于平动点任务的轨道设计.为了研究级数解的适用范围,最后对其收敛域进行了计算.Non-equilibrium point in the circular restricted three-body system can be changed into an artificial equilibrium point by means of low-thrust acceleration, and an spacecraft located at the artificial equilibrium point remains static relative to the primaries in the synodic coordinate system. In the classical restricted three-body system, the libration point orbit resource is limited, and the existence of artificial equilibrium point could overcome the shortage. The richness of artificial equilibrium points leads to the flexibility of mission design in deep space exploration. Due to the stability of stable artificial equilibrium points, for a spacecraft moving around them, less propellant is required for station keeping. In this paper, we expand the general motion around stable artificial equilibrium points as formal series of long-period, short-period and vertical periodic amplitudes. Then Lindstedt-Poincaré method is adopted to construct the series solutions up to an arbitrary order. By taking advantage of the series expansions constructed, the motions around artificial equilibrium points can be parameterized, and these parameters are beneficial to the optimization process of libration point mission design. At last, in order to provide the available range of series expansions constructed, the practical convergence is considered.

关 键 词：圆型限制性三体问题 人工平动点 周期轨道 

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]