平动点附近旋转三角形绳系卫星编队动力学
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摘要
绳系卫星编队飞行是21世纪的一个新的研究领域,国内外许多学者已经对此做了一些研究工作。相比传统的卫星,绳系卫星系统具有其独特的优势,如低成本、节省燃料、高性能、高灵活性等。相比一般的绳系卫星系统,三角形绳系卫星编队系统可以通过自身的旋转来保持系绳的张紧和系统的稳定,这样可以大大地节省系统在运行时所消耗的燃料。国外已经有了关于三角形绳系卫星的实验研究和相关报道,旋转三角形绳系卫星的研究具有非常重要的意义。
本文首先介绍了绳系卫星系统的基本概念、特点及其研究进展,讨论了研究三角形绳系卫星的意义等。然后详细介绍了建模过程中所要用到的基本理论和概念,如三体问题、平动点和微分修正法等。最后,通过建立合理有效的动力学模型,用数值方法研究了L2平动点附近的旋转三角形绳系卫星编队系统的动力学问题。
为了便于分析,我们假设三角形绳系卫星系统仅在日地系统平面内运动且只受引力的作用,且系绳始终保持为张紧状态,不计系绳的质量。基于这些假设,我们推导了L2平动点附近旋转三角形绳系卫星编队系统的动能和势能,将它们分别代入到拉格朗日方程中,最终得到了一组非线性姿轨耦合的动力学方程组。为了研究该三角形绳系卫星系统的稳定性,我们分别考虑了轨道高度、系绳长度和旋转速度对系统稳定性的影响,为此我们选用了两组经过微分修正法修正后的Lyapunov平面周期轨道的初始值,分别针对不同边长的初始形状为等边三角形的绳系卫星编队进行数值模拟,考虑在不同旋转速率下的系统的稳定性。模拟结果表明在不同的轨道上,系统的稳定性是不一样的,即轨道对系统的稳定性有一定的影响；系绳的长度几乎不影响系统质心的运动轨迹；另外,系统的旋转速率对其稳定性也有很大的影响,即旋转速率越大,系统的稳定性越好。实际中,旋转速率越大,系统的离心力也越大,进而系统的稳定性也越好。
Tethered satellite formation flying is a new area of research in the21st century and many scholars have done some research work about it. By comparing with the traditional satellite, the tethered satellite formation system has unique advantages, such as low-cost, low energy consumption, high performance, high flexibility, etc. Through its own rotation, triangular tethered satellite system can keep the tether tension and stability of the system which can greatly save the fuel consumption of the system compared with the traditional tethered satellite system. Some basic studies and experiments have been done about the triangular tethered satellite formation in abroad. This indicates that it has practical significance to investigate this system.
Firstly, we introduce the basic concepts, characteristics and the progress of the research of the tethered satellite formation in this dissertation. The significance to study the triangular tethered satellite has also been discussed. Then, the basic theories and concepts which will be used during the process of modeling are introduced in detail, such as three-body problem, libration points, differential correction method, etc. Finally, we study the stability of the rotating triangular tethered satellite formation system near the L2libration point through presenting a reasonably and effectively dynamical model of the system.
It is assumed that the system only moves in the plane of the Sun-Earth system, only the gravity is taken into consideration, and the tethers are always tension and without considering their masses for simplicity sake. Based on these assumptions, the kinetic and potential energy of the system near the L2libration point are derived. A set of high nonlinear coupling equations of the attitude motion and orbit motion are obtained by substituting the kinetic and potential energy into the Lagrange equation. In order to study the stability of the rotating triangular tethered satellite formation system, the effects of the orbital attitude, the tether length and the rotating rate on the stability of the system are considered respectively. We chose two sets of the initial values of the Lyapunov plane periodic orbit which are corrected by the differential correction method. Then, triangular tethered satellite formation system with different lengths of each side is simulated respectively. Different rotating rates are taken into account to analyze the stability of the system. The results of simulating demonstrate that the stability of the system is not the same in different orbits, i.e. the orbit altitude has some effects on the stability of the system. The length of tether almost does not affect the trajectory of the system center of mass. In addition, the rotation rate has a great influence on the stability of the system, i.e. the greater the rotation rate, the better the stability of the system. In fact, the larger the rotation rate is, the greater the system's centrifugal force is, and the system's stability is better as well.
本文首先介绍了绳系卫星系统的基本概念、特点及其研究进展,讨论了研究三角形绳系卫星的意义等。然后详细介绍了建模过程中所要用到的基本理论和概念,如三体问题、平动点和微分修正法等。最后,通过建立合理有效的动力学模型,用数值方法研究了L2平动点附近的旋转三角形绳系卫星编队系统的动力学问题。
为了便于分析,我们假设三角形绳系卫星系统仅在日地系统平面内运动且只受引力的作用,且系绳始终保持为张紧状态,不计系绳的质量。基于这些假设,我们推导了L2平动点附近旋转三角形绳系卫星编队系统的动能和势能,将它们分别代入到拉格朗日方程中,最终得到了一组非线性姿轨耦合的动力学方程组。为了研究该三角形绳系卫星系统的稳定性,我们分别考虑了轨道高度、系绳长度和旋转速度对系统稳定性的影响,为此我们选用了两组经过微分修正法修正后的Lyapunov平面周期轨道的初始值,分别针对不同边长的初始形状为等边三角形的绳系卫星编队进行数值模拟,考虑在不同旋转速率下的系统的稳定性。模拟结果表明在不同的轨道上,系统的稳定性是不一样的,即轨道对系统的稳定性有一定的影响；系绳的长度几乎不影响系统质心的运动轨迹；另外,系统的旋转速率对其稳定性也有很大的影响,即旋转速率越大,系统的稳定性越好。实际中,旋转速率越大,系统的离心力也越大,进而系统的稳定性也越好。
Tethered satellite formation flying is a new area of research in the21st century and many scholars have done some research work about it. By comparing with the traditional satellite, the tethered satellite formation system has unique advantages, such as low-cost, low energy consumption, high performance, high flexibility, etc. Through its own rotation, triangular tethered satellite system can keep the tether tension and stability of the system which can greatly save the fuel consumption of the system compared with the traditional tethered satellite system. Some basic studies and experiments have been done about the triangular tethered satellite formation in abroad. This indicates that it has practical significance to investigate this system.
Firstly, we introduce the basic concepts, characteristics and the progress of the research of the tethered satellite formation in this dissertation. The significance to study the triangular tethered satellite has also been discussed. Then, the basic theories and concepts which will be used during the process of modeling are introduced in detail, such as three-body problem, libration points, differential correction method, etc. Finally, we study the stability of the rotating triangular tethered satellite formation system near the L2libration point through presenting a reasonably and effectively dynamical model of the system.
It is assumed that the system only moves in the plane of the Sun-Earth system, only the gravity is taken into consideration, and the tethers are always tension and without considering their masses for simplicity sake. Based on these assumptions, the kinetic and potential energy of the system near the L2libration point are derived. A set of high nonlinear coupling equations of the attitude motion and orbit motion are obtained by substituting the kinetic and potential energy into the Lagrange equation. In order to study the stability of the rotating triangular tethered satellite formation system, the effects of the orbital attitude, the tether length and the rotating rate on the stability of the system are considered respectively. We chose two sets of the initial values of the Lyapunov plane periodic orbit which are corrected by the differential correction method. Then, triangular tethered satellite formation system with different lengths of each side is simulated respectively. Different rotating rates are taken into account to analyze the stability of the system. The results of simulating demonstrate that the stability of the system is not the same in different orbits, i.e. the orbit altitude has some effects on the stability of the system. The length of tether almost does not affect the trajectory of the system center of mass. In addition, the rotation rate has a great influence on the stability of the system, i.e. the greater the rotation rate, the better the stability of the system. In fact, the larger the rotation rate is, the greater the system's centrifugal force is, and the system's stability is better as well.
引文
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[3]Folta DC, Bordi F, Scolese C. Considerations on formation flying separations f( Earth observing satellite missions [C]. Proceedings of the AIAA/AAS Spacecraf Mechanics Meeting, AAS 92-144:803-822.
[4]Folta DC, Newman LK, David Q. Design and implementation of satellite formatioi and constellations [J]. AAS 98-304:57-70.
[5]Johnson L, Gilchrist B, Estes RD and Loremzini E. Overview of Future NASA Tethe Applications [J]. Advances in the Astronautical Sciences,1999,24(4):1055-1063
[6]苟兴宇,马兴瑞,邵成勋.绳系卫星系统研究概况[J].航天器工程,1995,4(4)：34-42
[7]谢永亮.辐射开环绳系卫星编队飞行的稳定性飞行[D].南京航空航天大学,硕士学位论文,2007年.
[8]刘丽丽,文浩,金栋平,胡海岩.三体绳系卫星面内编队飞行的回收控制[J].振动工程学报,2008,21(3)：223-227.
[9]文浩,金栋平,胡海岩.倾斜轨道电动力绳系卫星回收控制[J].力学学报,2008,40(3)375-380.
[10]金栋平,丁锋.绳系单体系统面内运动的定位控制[J].振动工程学报,2008,21(1)：1-6.
[11]王晓宇,金栋平.飞行时间不受约束的绳系卫星最优控制[J].应用力学学报,2009,26(4)：771-776.
[12]陈辉,文浩,金栋平,胡海岩.用弹性绳系系统进行空间捕捉的最优控制[J].宇航学报2009,30(2)：550-555.
[13]刘丽丽,文浩,金栋平,胡海岩.绳系卫星轨道转移的最优控制[J].航空学报,2009,30(2)：332-336.
[14]刘丽丽,文浩,金栋平,胡海岩.三维电动力绳系子卫星轨道转移的最优控制[J].计算力学学报,2011,28(2)：178-182.
[15]徐忠宾,金栋平.绳系单体系统鲁棒控制实验研究[J].应用力学学报,2010,27(3)：450-455.
[16]余本嵩,文浩,金栋平.时变自由度绳系卫星系统动力学[J].力学学报,2010,42(5)：926-932.
[17]王晓宇,金栋平.计入姿态的绳系卫星概周期振动[J].振动工程学报,2010,23(4)：361-365.
[18]文浩,金栋平,胡海岩.绳系卫星收放控制地面实验研究[J].振动工程学报,2010,23(1)：7-10.
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