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双体小行星系统平衡态与稳定性研究
杜燕茹1,2, 李翔宇1,2, 韩宏伟1,2, 乔栋1,2
1.北京理工大学 宇航学院, 北京 100081;2.深空自主导航与控制工信部重点实验室, 北京 100081
摘要:
由于双体小行星独特的运动形式可为行星的演化提供重要线索,因而成为小行星探测中的热点目标。基于双椭球体模型研究了双小行星系统的相对运动、平衡态及稳定性。首先基于双椭球的全二体模型建立了双星系统相对运动的动力学方程;其次利用拉格朗日方程,通过求解系统角动量和能量,建立了双星系统平衡态对应的状态约束;最后给出了通过零速度状态曲面判断双星系统平衡态稳定性的一般性方法,在此基础上分析了小行星物理参数变化对系统平衡态稳定性的影响。研究可为未来双体小行星系统探测任务中的轨道设计与控制提供重要的理论参考。
关键词:  双体小行星系统;双椭球模型;平衡态;稳定性
DOI:10.15982/j.issn.2095-7777.2019.05.006
分类号:V412.4
基金项目:国家自然科学基金(11572038);教育部长江学者支持计划
Study on Equilibrium and Stability of Binary Asteroid Systems
DU Yanru1,2, LI Xiangyu1,2, HAN Hongwei1,2, QIAO Dong1,2
1.School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China;2.Key Laboratory of Autonomous Navigation and Control for Deep Space Exploration, Ministry of Industry and Information Technology, Beijing 100081, China
Abstract:
The unique motion of binary asteroid systems provide important clues for the evolution of planets. Therefore, binary asteroid systems become hot targets in asteroid exploration. In this paper, based on the double ellipsoid model, the relative motion, equilibrium condition and stability of binary asteroid systems are studied. Firstly, the full two-body dynamic equation of the double ellipsoid model is established to describe the relative motion of a binary asteroid system. Secondly, the Lagrangian equation of motion is used to solve the angular momentum and energy of the system, and the equilibrium conditions are obtained. Finally, a method to determine the stability of equilibrium is given by using the zero-velocity state surface and the influence of the asteroid's physical parameter on the stability of equilibrium is analyzed. This research can provide a theoretical reference for the trajectory design and control in future exploration missions to binary asteroid systems.
Key words:  binary asteroid systems;double ellipsoid model;equilibrium;stability