深空探测中的轨道分析、设计与控制
|
摘要
本文以深空探测为背景,研究深空探测中与轨道相关的问题。根据目标天体的不同,研究方法也有所不同。本文主要有两部分：火星探测和小行星探测,它们分别代表大天体和小天体的探测,每一部分均涉及两种类型的轨道,即转移段轨道和环绕段轨道。
对于地球至火星的转移轨道,本文采用大推力转移和小推力转移两种手段进行研究。对于前者,由于火箭发射能力的限制,且从节省能量的角度,需要尽可能选择总耗费能量较小的时间窗口,然后利用经典的三段拼接方法得到简化力模型中的转移轨道,并给出各个变量之间的关系及其取值范围,以便能较快判断能否给出满足约束的轨道。对于满足约束的拼接轨道,利用微分修正法(即打靶法)获得实际力模型中的地火转移轨道。对于小推力转移轨道则有所不同,它对时间窗口的要求并不像大推力转移轨道那样严格,仅需要总转移时间合适即可。根据小推力转移轨道的特点,将整条轨道分成地心段、日心段和火心段三段,地心段和火心段的运行时间较长,因此采用以时间为优化指标的最优控制策略,通过对近似微分方程的求解,得到这个最优控制问题的近似解,从而将最优控制问题简化为计算量较小的轨道积分问题。日心段则采用燃料最优控制。针对每段的特点进行求解后,便可以通过调整时间变量将这三段轨道光滑地拼接起来,从而完成对小推力转移轨道的设计。
当探测器到达火星以后,便需要对环火轨道进行研究。火星与地球类似,是快自转行星,但火星引力场状态却与地球的状态有明显差别,其非球形引力位中的赤道椭率项J2，2接近于它的动力学扁率项J2，且其它谐系数也相对较大。因此在构造分析解的时候,联合项尤其是J2与J2，2的联合摄动不可忽视。除此之外,火星的两颗自然卫星距离火星较近,对于火星高轨卫星的影响不可忽视。而这两颗自然卫星没有像大行星那样完整的分析历表,这些均是本文需要解决的问题。文中推导了联合项摄动的分析公式和这两颗自然卫星的第三体摄动公式,建立了火星卫星的分析解,并将分析解应用到两颗自然卫星上,对公式进行简化和平滑掉短周期项后给出了平均历表的系数表达式,从而解决了所需要的两颗自然卫星的分析历表问题。将火星卫星分析解的结果和两颗自然卫星的分析历表与高精度的数值解对比,前者外推1-2d误差在500m的量级,而后者若要将误差控制在0(10-4)的量级,火卫一和火卫二的外推时间约为180d。
小行星探测一般为多目标多任务的探测,本文以三颗小行星为目标天体进行探测。由于小行星的引力范围较小,因此转移段的轨道设计相对于大行星较为简单,但涉及多颗目标天体,这便给最佳发射窗口的寻找带来一定的麻烦。本文按照约束条件和任务类型的特点,将整条轨道合理分成两段进行分别设计。对于小推力轨道的设计,先给出大推力转移轨道中消耗能量最小且转移时间适中的轨道,然后以小推力轨道替代,得到局部最优的方案。按照上述思想利用电推进和化学推进两种系统给出了两种满足约束的设计方案：全程电推进的轨道设计与化学推进和电推进相结合的轨道设计。本次设计方案的方法和软件同样适用于其它多目标深空轨道的设计,仅需要改变相应的参数即可。
除了飞越小行星以外,无论是环绕还是着陆小行星均需要研究小行星的伴飞轨道。而通常由于小行星质量太小、引力较弱,因此很难形成类似大行星卫星那样的环绕轨道。本文便针对伴飞弱引力小行星提出两种类型的伴飞轨道。第一种为小行星共线平动点附近Lissajous轨道和halo轨道;第二种为编队飞行轨道,直接伴飞小行星。由于这两种轨道与小行星的距离适中,因此不需要考虑小行星非球形引力摄动的影响,从而在对小行星资料了解不足的情况下可以作为中间任务轨道。文中首先给出这两种轨道的分析解,然后以分析解为初值,利用多点打靶法进行轨道修正得到实际力模型中的轨道。这两种轨道均是不稳定的,需要对其进行轨道控制。本文采用了小推力控制和太阳帆板控制两种手段,所用的优化控制方法为最优线性反馈控制。对于太阳帆板控制,给出如下两种控制策略：一是固定太阳帆的面质比改变它的俯仰角和偏航角,另一是固定太阳帆的俯仰角和偏航角改变而质比。结果表明对于这两种类型的中间任务轨道,上述控制方案均可行。对于太阳帆板控制,改变太阳帆板面积的控制策略只能使得控制后的轨道在标称轨道一定距离附近振荡,因此控制效果不如改变方向角的控制策略。
This paper studies the issues about orbit analysis and orbit design in deep space explorations. There are two parts—Mars explorations and asteroid explorations. Each part includes two types of orbits, the transfer orbits and the orbits around target bodies.
The chemical propulsion system and the electric propulsion system are used to design the Earth-Mars transfer orbits. For the former, the launch windows of low-energy orbits in the simplified two-body model are chosen for the restrictions of fuel and the launch capacity of the rocket. Then the classical patched conic method is employed to obtain the two-body transfer orbits of three sections. Afterwards, the relations of how the variables influence each other are studied before we can judge quickly whether the suitable orbit can be given or not. However, for the low-thrust transfer orbit, the transfer time has only to be matched with low-thrust. The whole Earth-Mars low-thrust orbit is divided into three parts according to the property of low-thrust orbit. The transfer time within the gravisphere of either the Earth or the Mars is so long that the optimal control strategy minimizing the time is adopted. The approximate solution is obtained by solving the approximate differential equations. Therefore, the optimal control problem is simplified into orbit integrations. For the Sun-centered section, the optimal fuel orbit is preferred. After that, the three sections can be patched smoothly by adjusting the transfer time slightly.
The orbits around the Mars should be studied after the probe is captured by the Mars. Similar to the Earth, the Mars rotates fast. However, the gravitational field of the Mars is quite different from that of the Earth. The coefficient J2,2is very close to J2and other coefficients are also larger compared with those of the Earth, so the coupled perturbations especially that of J2and J2,2cannot be neglected in analytical solution. Besides, both of the two natural satellites of the Mars are close to the Mars, hence their perturbations for the high-altitude satellites are not negligible. Nevertheless, there are no publications concerning the analytical ephemerides of the two natural satellites. Both of the two problems need to be solved. In this paper, the analytical formulae of the coupled perturbations and the natural satellites'perturbations are derived, and the analytical solution of the Mars probe is constructed. Then the analytical solutions of the two natural satellites are given. After simplifying the formulae and abandoning the short-period terms, the coefficients of the analytical ephemerides can be obtained. At last, the numerical solutions are provided to verify the precisions of the analytical solution and the analytical ephemerides. The results show that the position error of the low-altitude satellite is about500m with the duration of1-2d. For the natural satellites, the appropriate duration is about180d for Phobos and Deimos if the error needed to be within O(10-4).
Most of small body explorations are of the type of multiple targets and multitasking, so the paper uses three asteroids as the target bodies, flying by the first one and circling around or accompanying the second one and the third one. Different from the planets, the design of the transfer orbit is relatively simple for the gravitational scopes of most asteroids are so small that can be neglected. However, the difficulty is to find out the optimal launch window of exploring multiple asteroids. This paper divided the whole transfer orbit into two sections reasonably according to the restrictions and the properties of task type. For each section, the chemical propulsion orbit with low energy and moderate duration is obtained and then optimized using low-thrust. On the basis of the methods above, two kinds of orbits are given with chemical propulsion and electric propulsion—the low-thrust orbit and the orbit with both high and low thrust. Besides, the methods and software are also applicable for other deep space orbit design.
The gravity fields of the asteroids are mostly very small and irregular, so it is necessary to study the orbits around them with special treatment. In the paper, two kinds of intermediate orbits for asteroid explorations are proposed. One is around the collinear libration points of the Sun-asteroid restricted three-body problem. The other is around the asteroid itself. The first kind of intermediate orbit is applicable to asteroids with known masses, while the second is suitable for asteroids with unknown or negligible masses. Analytical solutions of these two intermediate orbits in the simplified models are introduced first, and then numerical algorithms are used to refine them to obtain the true orbits in the real force model. At last, the problem of station-keeping is addressed. Both of low-thrust control and solar sail control are used. The solar sail control strategy includes varying the solar sail area and varying the pitch angle and the yaw angle. The linear optimal feedback control law is considered, and numerical simulations are made to both kinds of intermediate orbits. The results show that both kinds of orbits are feasible. For low-thrust control strategy, the cost is reasonable and mainly depends on the initial insertion error. For the other one, the technique of varying the pitch angle and the yaw angle is better than varying the solar sail area.
对于地球至火星的转移轨道,本文采用大推力转移和小推力转移两种手段进行研究。对于前者,由于火箭发射能力的限制,且从节省能量的角度,需要尽可能选择总耗费能量较小的时间窗口,然后利用经典的三段拼接方法得到简化力模型中的转移轨道,并给出各个变量之间的关系及其取值范围,以便能较快判断能否给出满足约束的轨道。对于满足约束的拼接轨道,利用微分修正法(即打靶法)获得实际力模型中的地火转移轨道。对于小推力转移轨道则有所不同,它对时间窗口的要求并不像大推力转移轨道那样严格,仅需要总转移时间合适即可。根据小推力转移轨道的特点,将整条轨道分成地心段、日心段和火心段三段,地心段和火心段的运行时间较长,因此采用以时间为优化指标的最优控制策略,通过对近似微分方程的求解,得到这个最优控制问题的近似解,从而将最优控制问题简化为计算量较小的轨道积分问题。日心段则采用燃料最优控制。针对每段的特点进行求解后,便可以通过调整时间变量将这三段轨道光滑地拼接起来,从而完成对小推力转移轨道的设计。
当探测器到达火星以后,便需要对环火轨道进行研究。火星与地球类似,是快自转行星,但火星引力场状态却与地球的状态有明显差别,其非球形引力位中的赤道椭率项J2，2接近于它的动力学扁率项J2，且其它谐系数也相对较大。因此在构造分析解的时候,联合项尤其是J2与J2，2的联合摄动不可忽视。除此之外,火星的两颗自然卫星距离火星较近,对于火星高轨卫星的影响不可忽视。而这两颗自然卫星没有像大行星那样完整的分析历表,这些均是本文需要解决的问题。文中推导了联合项摄动的分析公式和这两颗自然卫星的第三体摄动公式,建立了火星卫星的分析解,并将分析解应用到两颗自然卫星上,对公式进行简化和平滑掉短周期项后给出了平均历表的系数表达式,从而解决了所需要的两颗自然卫星的分析历表问题。将火星卫星分析解的结果和两颗自然卫星的分析历表与高精度的数值解对比,前者外推1-2d误差在500m的量级,而后者若要将误差控制在0(10-4)的量级,火卫一和火卫二的外推时间约为180d。
小行星探测一般为多目标多任务的探测,本文以三颗小行星为目标天体进行探测。由于小行星的引力范围较小,因此转移段的轨道设计相对于大行星较为简单,但涉及多颗目标天体,这便给最佳发射窗口的寻找带来一定的麻烦。本文按照约束条件和任务类型的特点,将整条轨道合理分成两段进行分别设计。对于小推力轨道的设计,先给出大推力转移轨道中消耗能量最小且转移时间适中的轨道,然后以小推力轨道替代,得到局部最优的方案。按照上述思想利用电推进和化学推进两种系统给出了两种满足约束的设计方案：全程电推进的轨道设计与化学推进和电推进相结合的轨道设计。本次设计方案的方法和软件同样适用于其它多目标深空轨道的设计,仅需要改变相应的参数即可。
除了飞越小行星以外,无论是环绕还是着陆小行星均需要研究小行星的伴飞轨道。而通常由于小行星质量太小、引力较弱,因此很难形成类似大行星卫星那样的环绕轨道。本文便针对伴飞弱引力小行星提出两种类型的伴飞轨道。第一种为小行星共线平动点附近Lissajous轨道和halo轨道;第二种为编队飞行轨道,直接伴飞小行星。由于这两种轨道与小行星的距离适中,因此不需要考虑小行星非球形引力摄动的影响,从而在对小行星资料了解不足的情况下可以作为中间任务轨道。文中首先给出这两种轨道的分析解,然后以分析解为初值,利用多点打靶法进行轨道修正得到实际力模型中的轨道。这两种轨道均是不稳定的,需要对其进行轨道控制。本文采用了小推力控制和太阳帆板控制两种手段,所用的优化控制方法为最优线性反馈控制。对于太阳帆板控制,给出如下两种控制策略：一是固定太阳帆的面质比改变它的俯仰角和偏航角,另一是固定太阳帆的俯仰角和偏航角改变而质比。结果表明对于这两种类型的中间任务轨道,上述控制方案均可行。对于太阳帆板控制,改变太阳帆板面积的控制策略只能使得控制后的轨道在标称轨道一定距离附近振荡,因此控制效果不如改变方向角的控制策略。
This paper studies the issues about orbit analysis and orbit design in deep space explorations. There are two parts—Mars explorations and asteroid explorations. Each part includes two types of orbits, the transfer orbits and the orbits around target bodies.
The chemical propulsion system and the electric propulsion system are used to design the Earth-Mars transfer orbits. For the former, the launch windows of low-energy orbits in the simplified two-body model are chosen for the restrictions of fuel and the launch capacity of the rocket. Then the classical patched conic method is employed to obtain the two-body transfer orbits of three sections. Afterwards, the relations of how the variables influence each other are studied before we can judge quickly whether the suitable orbit can be given or not. However, for the low-thrust transfer orbit, the transfer time has only to be matched with low-thrust. The whole Earth-Mars low-thrust orbit is divided into three parts according to the property of low-thrust orbit. The transfer time within the gravisphere of either the Earth or the Mars is so long that the optimal control strategy minimizing the time is adopted. The approximate solution is obtained by solving the approximate differential equations. Therefore, the optimal control problem is simplified into orbit integrations. For the Sun-centered section, the optimal fuel orbit is preferred. After that, the three sections can be patched smoothly by adjusting the transfer time slightly.
The orbits around the Mars should be studied after the probe is captured by the Mars. Similar to the Earth, the Mars rotates fast. However, the gravitational field of the Mars is quite different from that of the Earth. The coefficient J2,2is very close to J2and other coefficients are also larger compared with those of the Earth, so the coupled perturbations especially that of J2and J2,2cannot be neglected in analytical solution. Besides, both of the two natural satellites of the Mars are close to the Mars, hence their perturbations for the high-altitude satellites are not negligible. Nevertheless, there are no publications concerning the analytical ephemerides of the two natural satellites. Both of the two problems need to be solved. In this paper, the analytical formulae of the coupled perturbations and the natural satellites'perturbations are derived, and the analytical solution of the Mars probe is constructed. Then the analytical solutions of the two natural satellites are given. After simplifying the formulae and abandoning the short-period terms, the coefficients of the analytical ephemerides can be obtained. At last, the numerical solutions are provided to verify the precisions of the analytical solution and the analytical ephemerides. The results show that the position error of the low-altitude satellite is about500m with the duration of1-2d. For the natural satellites, the appropriate duration is about180d for Phobos and Deimos if the error needed to be within O(10-4).
Most of small body explorations are of the type of multiple targets and multitasking, so the paper uses three asteroids as the target bodies, flying by the first one and circling around or accompanying the second one and the third one. Different from the planets, the design of the transfer orbit is relatively simple for the gravitational scopes of most asteroids are so small that can be neglected. However, the difficulty is to find out the optimal launch window of exploring multiple asteroids. This paper divided the whole transfer orbit into two sections reasonably according to the restrictions and the properties of task type. For each section, the chemical propulsion orbit with low energy and moderate duration is obtained and then optimized using low-thrust. On the basis of the methods above, two kinds of orbits are given with chemical propulsion and electric propulsion—the low-thrust orbit and the orbit with both high and low thrust. Besides, the methods and software are also applicable for other deep space orbit design.
The gravity fields of the asteroids are mostly very small and irregular, so it is necessary to study the orbits around them with special treatment. In the paper, two kinds of intermediate orbits for asteroid explorations are proposed. One is around the collinear libration points of the Sun-asteroid restricted three-body problem. The other is around the asteroid itself. The first kind of intermediate orbit is applicable to asteroids with known masses, while the second is suitable for asteroids with unknown or negligible masses. Analytical solutions of these two intermediate orbits in the simplified models are introduced first, and then numerical algorithms are used to refine them to obtain the true orbits in the real force model. At last, the problem of station-keeping is addressed. Both of low-thrust control and solar sail control are used. The solar sail control strategy includes varying the solar sail area and varying the pitch angle and the yaw angle. The linear optimal feedback control law is considered, and numerical simulations are made to both kinds of intermediate orbits. The results show that both kinds of orbits are feasible. For low-thrust control strategy, the cost is reasonable and mainly depends on the initial insertion error. For the other one, the technique of varying the pitch angle and the yaw angle is better than varying the solar sail area.
引文
[1]http://nssdc.gsfc.nasa.gov/planetary/chronology_mars.html
[2]http://burro.astr.cwru.edu/stu/advanced/20th_soviet_mars.html
[3]http://burro.astr.cwru.edu/stu/advanced/20th_far_mariner.html
[4]Ulivi, Paolo, Harland, David M., Robotic Exploration of the Solar System Part I:The Golden Age 1957-1982, Praxis,2007
[5]http://www.astronautix.com/craft/marner34.htm
[6]http://www.astronautix.com/project/mars.htm
[7]http://zh.wikipedia.org/wiki/%E7%81%AB%E6%98%9F2%E5%8F%B7
[8]Harvey, Brian,Russian Planetary Exploration History, Development, Legacy and Prospects, 2007, Springer/Praxis
[9]ASIF A. SIDDIQI,Deep Space Chronicle-A Chronicle of Deep Space and Planetary Probes, Monographs in Aerospace History,2002.6
[10]http://zh.wikipedia.org/zh-cn/%E7%B6%AD%E4%BA%AC%E8%99%9F%E8%A8%88%E 5%8A%83
[11]http://nssdc.gsfc.nasa.gov/nmc/masterCatalog.do?sc=1975-075A
[12]http://zh.wikipedia.org/zh-cn/%E6%B5%B7%E7%9B%9C2%E8%99%9F
[13]http://nssdc.gsfc.nasa.gov/nmc/masterCatalog.do?sc=1975-083A
[14]http://en.wikipedia.org/wiki/Phobos_program
[15]http://www.hudong.com/wiki/%E7%81%AB%E6%98%9F%E8%A7%82%E5%AF%9F%E8 %80%85
[16]http://en.wikipedia.org/wiki/Mars_Observer
[17]http://en.wikipedia.org/wiki/Mars_Global_Surveyor
[18]http://nssdc.gsfc.nasa.gov/nmc/spacecraftOrbit.do?id= 1996-062A
[19]http://nssdc.gsfc.nasa.gov/planetary/text/mars96_timeline.txt
[20]http://en.wikipedia.org/wiki/Mars_96
[21]http://www.msss.com/mars/mars9x/mission.html
[22]http://mars.jpl.nasa.gov/MPF/mpf/mpfcruise.html
[23]http://burro.astr.cwru.edu/stu/advanced/20th_far_pathfinder.html
[24]http://en.wikipedia.org/wiki/Nozomi_(probe)
[25]http://www.astronautix.com/details/mar12378.htm
[26]http://en.wikipedia.org/wiki/Mars_Polar_Lander
[27]R.S.Saunders et.al.2001 Mars Odyssey Mission Summary, Space Science Reviews, Vol.110, N.O.1-2/2004.01.Available at website "http://www.springerlink.com/content/t4v8wvlwr 52265g2/"
[28]http://nssdc.gsfc.nasa.gov/nmc/masterCatalog.do?sc=2003-022A
[29]http://sci.esa.int/science-e/www/object/index.cfm?fobjectid=31037
[30]http://zh.wikipedia.org/wiki/%E5%8B%87%E6%B0%94%E5%8F%B7
[31]http://nssdc.gsfc.nasa.gov/nmc/masterCatalog.do?sc=2003-027A
[32]Mars Exploration Rover Launches,Press Kit,2003.06
[33]http://nssdc.gsfc.nasa.gov/nmc/masterCatalog.do?sc=2003-032A
[34]http://nssdc.gsfc.nasa.gov/nmc/masterCatalog.do?sc=2005-029A
[35]http://en.wikipedia.org/wiki/Phoenix_(spacecraft)
[36]http://nssdc.gsfc.nasa.gov/nmc/masterCatalog.do?sc=2007-034A
[37]http://www.dmuller.net/phoenix/
[38]Emily Lakdawalla. Phobos-Grunt Failure Report Released. Planetary Society. Feb.6,2012 [2012-02-08].
[39]http://zh.wikipedia.org/wiki/%E7%A6%8F%E5%B8%83%E6%96%AF%EF%BC%8D%E5 %9C%9F%E5%A3%A4
[40]http://zh.wikipedia.org/wiki/%E8%90%A4%E7%81%AB%E4%B8%80%E5%8F%B7
[41]http://zh.w ikipedia.org/wiki/%E7%81%AB%E6%98%9F%E7%A7%91%E5%AD%A6%E5 %AE%9E%E9%AA%8C%E5%AE%A4
[42]胡寿村,刘林,火星探测飞行轨道综述,中国宇航学会第25届飞行器测控学术年会论文集,2010。
[43]http://solarsystem.nasa.gov/missions/profile.cfm?MCode=ISEEICE
[44]http://nssdc.gsfc.nasa.gov/nmc/spacecraftDisplay.do?id=1978-079A
[45]ICE Encounter Operations, N.Fanelli & D.Morris
[46]http://www.mentallandscape.com/V_Vega.htm
[47]http://en.wikipedia.org/wiki/Giotto_(spacecraft)
[48]http://zh.wikipedia.org/wiki/%E5%96%AC%E6%89%98%E8%99%9F
[49]http://en.wikipedia.org/wiki/Galileo_(spacecraft)
[50]http://zh.wikipedia.org/wiki/%E4%BC%BD%E5%88%A9%E7%95%A5%E5%8F%B7%E6 %8E%A2%E6%B5%8B%E5%99%A8
[51]NEAR Shoemaker Spacecraft Mission Operations, Mark E. Holdridge
[52]http://near.jhuapl.edu/NewMissionDesign/orbPlan0516.html
[53]Recovery of NEAR's Mission to Eros.
[54]http://www.bjp.org.cn/otherpage/eros/erosl.html
[55]http://zh.wikipedia.org/wiki/%E6%B7%B1%E7%A9%BA%E4%B8%80%E8%99%9F
[56]http://en.wikipedia.org/wiki/Deep_Space_1
[57]http://zh.wikipedia.org/wiki/%E6%98%9F%E5%B0%98%E5%8F%B7
[58]http://en.wikipedia.org/wiki/Stardust_(spacecraft)
[59]http://en.wikipedia.org/wiki/CONTOUR
[60]http://zh.wikipedia.org/wiki/%E9%9A%BC%E9%B8%9F%E5%8F%B7
[61]http://en.wikipedia.org/wiki/Hayabusa
[62]http://zh.wikipedia.org/wiki/%E8%8F%B2%E8%90%8A%E6%8E%A2%E6%B8%AC%E5 %99%A8
[63]http://en.wikipedia.org/wiki/Rosetta_(spacecraft)
[64]http://zh.wikipedia.org/wiki/%E6%B7%B1%E5%BA%A6%E6%92%9E%E5%87%BB%E5 %8F%B7
[65]http://en.wikipedia.org/wiki/Deep_Impact_(spacecraft)
[66]http://zh.wikipedia.org/wiki/%E6%9B%99%E5%85%89%E8%99%9F
[67]http://en.wikipedia.org/wiki/Dawn_(spacecraft)
[68]http://en.wikipedia.org/wiki/Cassini%E2%80%93Huygens
[69]http://zh.wikipedia.org/wiki/%E5%8D%A1%E8%A5%BF%E5%B0%BC-%E6%83%A0%E6 %9B%B4%E6%96%AF%E5%8F%B7
[70]http://en.wikipedia.org/wiki/New_Horizons
[71]http://zh.wikipedia.org/wiki/%E6%96%B0%E8%A6%96%E9%87%8E%E8%99%9F
[1]刘林,胡松杰,王歆.航天动力学引论[M].南京：南京大学出版社,2006.
[2]Archinal, B.A., A'Hearn, M.F., Bowell, E., et al., Report of the IAU working group on cartographic coordinates and rotational elements:2009. Celest. Mech. Dyn. Astron.2011, 109:101-135.
[3]刘林,赵玉晖,张巍等,火星卫星运动的坐标系附加摄动及相应坐标系的选择.天文学报,2010,51(4)：412-421.
[4]Liu Lin, Zhao Yu-hui, Zhang Wei, et al., Coordinate Additional Perturbations to Mars Orbiters and Choice of Corresponding Coordinate System. Chinese Astronomy and Astrophysics, 2011,35(2):188-198.
[1]Battin, R.H., An Introduction to the Mathematics and Methods of Astrodynamics, American Institute of Aeronautics and Astronautics, Inc. New York, New York.1987.
[2]Gooding, R.H., On the Solution of Lambert's Orbital Boundary-Value Problem. RAE Technical Report 88027,1988.
[3]张旭辉,刘竹生,火星探测器轨道设计与优化技术,导航与航天运载技术,第2期(总第294期)：15-23,2008.
[4]赵国强,宝音贺西,李俊峰,基于B平面的火星探测直接转移轨道设计方法,中国空间科学技术,第1期：1-7,2012年2月.
[5]高飞,火星探测直接转移轨道精确求解研究,空间科学学报,30(6)：519-523,2010.
[6]陈杨,赵国强,宝音贺西,李俊峰,精确动力学模型下的火星探测轨道设计,中国空间科学技术,第1期：8-15,2012年2月.
[7]高飞,火星探测直接转移轨道设计研究,航天控制,28(4)：48-53,2010年8月.
[8]李云飞,行星际探测器轨道设计。南京大学天文系,天体测量与天体力学硕士论文。
[9]Hanspeter Schaub and John L. Junkins, Analytical Mechanics of Aerospace Systems (Chap. 12). January 1,2002
[10]尚海滨,崔平远,栾恩杰,地球-火星的燃料最省小推力转移轨道的设计与优化.宇航学报,27(6),1168-1173,2006年11月.
[11]尚海滨,崔平远,栾恩杰,星际小推力转移轨道快速设计方法,航空学报,28(6)：1281-1286,2007年11月.
[12]任远,崔平远,栾恩杰,利用混合法进行地球-火星小推力轨道设计,哈尔滨工业大学学报,39(3)：359-362,2007年3月.
[13]张旭辉,刘竹生,火星探测最优小推力变轨,导弹与航天运载技术,第1期(总第299期)：1-6,2009.
[14]R. Bertrand, J. Bernussou, Electric transfer optimization for Mars sample return mission, Acta Astronautica, Vol.48, No.5-12, pp.651-660,2011.
[15]G. Mingotti, F. Topputo, F. Bernelli-Zazzera, Earth-Mars transfers with ballistic escape and low-thrust capture, Celest Mech Dyn Astr (2011) 110:169-188
[16]任远,星际探测中的小推力转移轨道设计与优化方法研究,哈尔滨工业大学工学博士论文,2007年7月.
[17]李国勇等,最优控制理论及参数优化[M].北京,国防工业出版社,2006.1.
[1]Kozai Y., The motion of a close earth satellite. Astron. J.,1959,64(9):367-377
[2]Cook G. E., Basic theory for prod, a program for computing the development of satellite orbits. Celest. Mech,1973,7(3):301-314
[3]刘林,人造地球卫星轨道力学。高等教育出版社,1992.8。
[4]刘林,人造地球卫星在临界角附近运动的解。天文学报,1974,15(2)：230-240
[5]Liu Lin, A solution of the motion of an artificial satellite in the vicinity of the critical inclination. Chinese Astronomy,1977, 1(1):31-42.
[6]刘林,朱文耀,黄珹,人卫运动理论及其应用(Ⅰ)。天文学进展,1988,6(1)：42-51
[7]刘林,赵德滋,人造地球卫星运动中的共振问题。南京大学学报(自然科学版),1980,3：56-62
[8]张巍,刘林,关于地球飞行运动中的坐标系附加摄动问题。飞行器测控学报,2003,22(2)：25-29
[9]汤靖师,刘林,近地卫星运动的坐标系附加摄动在拟平均根数法中的处理。天文学报,2010.1,51(1)
[10]Jing-shi Tang, Lin Liu, The Application of Quasi-Mean-Element-Method to LEO under Additional Perturbation due to Change of Coordinate System. Chinese Astronomy and Astrophysics,2010,34(4):424-433.
[11]马剑波,刘林,王歆,地球非球形引力位中田谐项摄动的有关问题。天文学报,2001.11,42(4)
[12]Jian-bo Ma, Lin Liu, Xin Wang, Problems concerning the perturbation due to the tesseral harmonic terms in the nonspherical gravitational potential of the earth. Chinese Astronomy and Astrophysics,2002,26(2):235-244.
[13]刘林,王家松,月球卫星轨道变化的分析解。天文学报,39(1),1998.2
[14]Lin Liu, Jia-song Wang, An analytic solution of the orbital variation of lunar satellites. Chinese Astronomy and Astrophysics,1998,22(3):328-351.
[15]刘林,王歆,月球探测器轨道力学。国防工业出版社,2006.9
[16]刘林,C. K. Shum,在非球形引力摄动下金星轨道器运动的分析解。中国科学(A),29(10)：952-960,1999.10
[17]章圣泮,刘林,土卫七的运动理论。天文学报,23(2),1982.6
[18]Zhang Sheng-pan, Liu Lin, Theory of motion of hyperion. Chinese Astronomy and Astrophysics,1982,6(3):233-242.
[19]张伟,刘林,关于土卫八运动的轨道解。紫金山天文台台刊,18(1),1999-3
[20]刘世元,刘春保,刘林,卫星轨道变化规律的综合分析。飞行器测控学报,24(3),2005.6
[21]刘林,王歆,月球卫星轨道力学综述。天文学进展,21(4),2003.12
[22]王歆,刘林,制约卫星轨道寿命的另一种机制。天文学报,43(2),2002.5
[23]Xin Wang, Lin Liu, Another mechanism of restricting the lifetime of orbiting satellites. Chinese Astronomy and Astrophysics,2002,26(4):489-496.
[24]王歆,刘林,制约卫星轨道寿命的另一种机制(续)。天文学报,43(4),2002.11
[25]Xin Wang, Lin Liu, Another mechanism of restricting the lifetime of orbiting satellites (continued). Chinese Astronomy and Astrophysics,2003,27(1):107-113.
[26]王歆,刘林,目标天体极轨道卫星的轨道寿命。宇航学报,2001.9,22(5)
[27]刘林,王海红,关于月球低轨卫星运动的两个问题。天文学报,2006.7,47(3)
[28]Liu Lin, Wang Hai-hong, Two problems about the motion of low-moon-orbit satellites. Chinese Astronomy and Astrophysics,2006,30(4):437-446.
[29]刘林,汤靖师,火星轨道器运动的轨道变化特征。宇航学报,2008.3,29(2)
[30]刘林,王海红,胡松杰.人造地球卫星精密定轨(研究生用教材).南京：南京大学天文系,2005.
[31]刘林,航天器轨道理论.北京：国防工业出版社,2000.
[32]刘林,胡松杰,王歆.航天动力学引论.南京：南京大学出版社,2006.
[33]刘林,赵玉晖,张巍等,火星卫星运动的坐标系附加摄动及相应坐标系的选择.天文学报,2010,51(4)：412-421.
[34]Liu Lin, Zhao Yu-hui, Zhang Wei, et al., Coordinate Additional Perturbations to Mars Orbiters and Choice of Corresponding Coordinate System. Chinese Astronomy and Astrophysics,2011,35(2):188-198.
[35]Fehlberg E, Classical Fifth-, Sixth-, Seventh-and Eig-hth Order Runge-Kutta Formulas with Stepsize Contr-ol, NASA TR R-287,1968.
[36]P. Kenneth Seidelmann, B. A. Archinal, M. F. A'hearn, et al. Report of the IAU/IAG Working Group on cartographic coordinates and rotational elements[J]:2006. Celestial Mech Dyn Astr (2007)98:155-180
[37]Jon. Giorgini. Horizons On-Line Ephemeris System[DB/OL]. (2010-01-15) [2010-07-14]. http://ssd.jpl.nasa.gov/horizons.cgi.
[1]http://ssd.jpl.nasa.gov/sbdb.cgi#top
[2]http://comets-asteroids.findthedata.org/1/15723/12711-Tukmit-1991-BB
[3]http://ssd.jpl.nasa.gov/sbdb.cgi?sstr=99942;orb=0;cov=1;log=0;cad=0#elem
[4]http://neo.jpl.nasa.gov/risk/a99942.html
[5]http://ssd.jpl.nasa.gov/sbdb.cgi?sstr=1996fg3;orb=0;cov=1;log=0;cad=0#elem
[6]http://www.johnstonsarchive.net/astro/astmoons/am-175706.html
[7]Gooding, R.H. On the Solution of Lambert's Orbital Boundary-Value Problem. RAE Technical Report 88027,1988
[8]李国勇等,最优控制理论及参数优化[M].北京,国防工业出版社,2006.1.
[9]任远,星际探测中的小推力转移轨道设计与优化方法研究,哈尔滨工业大学工学博士论文,2007年7月.
[10]任远,崔平远,栾恩杰.基于标称轨道的小推力轨道设计方法.吉林大学学报(工学版),2006,36(6)：998-1002.
[1]Szebehely, V. Theory of Orbits. Academic Press, New York and London,1967
[2]刘林,胡松杰,王歆.航天动力学引论.南京：南京大学出版社,2006
[3]Gomez, G., Jorba, A., Masdemont, J., Simo, C.:Dynamics and Mission Design near Libration Point Orbits, Vol. Ⅲ, Advanced Methods for Collinear Points. World Scientific, Singapore (2001).
[4]Jorba A, Masdemont J., Dynamics in the centre manifold of the collinear points of the restricted three body problem, Physica D,132:189-213(1999).
[5]Richardson D.L.,1980, Analytic Construction of Periodic Orbits about the Collinear Points, Celestial Mechanics and Dynamical Astronomy, Vol 22,241-253
[6]Farquhar R. W., The Moon's influence on the location of the Sun-Earth exterior libration point, Celestial Mechanics,2:131-133,1970.
[7]Richardson D.L. and Cary N. D., A uniformly valid solution for motion about the interior libration point of the perturbed elliptic-restricted problem. In AAS/AIAA Astrodynamics Specialist Conference, AAS Paper 75-021,, July 1975.
[8]Farquhar R. W. and Kamel A. A., Quasi-periodic orbits about the translunar libration point, Celestial Mechanics,7:458-473,1973.
[9]Hou X.Y. and Liu L., On quasi-periodic motions around the triangular libration points of the real Earth-Moon system. Celestial Mechanics and Dynamical Astronomy, (2010) 108: 301-313.
[10]Hou X.Y. and Liu L., On quasi-periodic motions around the collinear libration points in the real Earth-Moon system. Celestial Mechanics and Dynamical Astronomy, (2011) 110:71-98.
[11]Gomez, G., Llibre J., Martinez R., and Simo, C.:Dynamics and Mission Design near Libration Point Orbits, Vol. I, Fundamentals:The Case of Collinear Libration Points. World Scientific, Singapore (2001).
[12]E. W. Brown and C. A. Shook. Planetary Theory. Dover,1964.
[13]Cheng A.F., Near Earth Asteroid Rendezvous:Mission Summary. Asteroids Ⅲ, W.F. Bottke Jr., A. Cellino, P. Paolicchi, and R. P. Binzel (eds), University of Arizona Press, Tucson, 351-366,2002.
[14]Thomas V.C., Makowski J.M., and Brown G.M. et al., The Dawn Spacecraft. Space Science Reviews, Volume 163, Issue 1-4,175-249,2011.
[15]Yoshikawa Makoto, Fujiwara Akira, Kawaguchi Jun'ichiro, Hayabusa and its adventure around the tiny asteroid Itokawa. Highlights of Astronomy, Volume 14,323-324,2007.
[16]Richardson D. L., Halo Orbit Formulation for the ISEE-3 Mission. Journal of Guidance and Control, Vol.3, No.6,1980, pp.543-548.
[17]Folda D., Vaughn F., A survey of Earth-Moon libration orbits:stationkeeping strategies and intra-orbit transfers. In:AIAA 2004-4741, AIAA/AAS Astrodynamics Specilist Conference, Providence, Rhode Island,2004.
[18]Kim M.,2001, Periodic Spacecraft Orbits for Future Space-Based Deep Space Observations Technique Report., Vienna Institute of Technology, Vienna, Astria
[19]G6mez G, Masdemont J. and Sim6 C, Quasi-Halo Orbits Associated with Libration Points. Journal of Astronautics Science,42(2):135-176(1998).
[20]Howell K.C. and Pernicka H.J., Numerical Determination of Lissajous Trajectories in the Restricted Three-Body Problem, Celestial Mechanics and Dynamical Astronomy,41: 107-124(1987).
[21]Morrison D.D., Riley J.D. and Zancanzro J.F., Multiple Shooting Method for Two-Point Boundary Value Problem, Communications of the ACM,5,12,613-614(1962).
[22]侯锡云,博士毕业论文.南京大学,2008
[23]Liu Lin, Wang Haihong, Ma Jianbo, On the Formation Flying of Satellite Constellations. Chin. Astro. Astrophy.,2004,28(2):188-199.
[24]刘林,侯锡云,轨道力学(研究生用教材),南京大学天文学系,2007.08
[25]Farquhar R.W., The control and use of libration point satellites. Technical Report TR R346, NASA,1970.
[26]Breakwell, J.V., Kamel, A.A., and Ratner M.J., Station-keeping for a translunar communications station. Celestial Mechanics,10(3):357-373,1974.
[27]Howell K.C, Pernicka H.J. Stationkeeping method for libration point trajectories. J. Guid. Control Dynam.16(1):151-159,1993.
[28]Gomez G., Howell K., Masdemont J., et al. Station-keeping strategies for translunar libration point orbits. Adv. Astronaut. Sci.99:949-967,1998.
[29]Anderson R.L., Lo M.W., Born G.H. Application of local Lyapunov exponents to maneuver design and navigation in the three-body problem, in:AAS 03-569, AIAA/AAS Astrodynamics Specialist Conf., Big Sky, Montana, USA, Aug 3-7,2003.
[30]Folta D., Vaughn F. A survey of Earth-Moon libration orbits:stationkeeping strategies and intra-orbit Transfers, in:AIAA 2004-4741, AIAA/AAS Astrodynamics Specialist Conf., Providence, Rhode Island, USA, Aug 16-19,2004.
[31]Kulkarni J.E., Campbell M.E., Dullerud G.E. Stabilization of spacecraft flight in halo orbits: an H∞ approach. IEEE. Trans. Control Syst. Technol.14(3):572-578,2006.
[32]Hou X.Y. and Liu L., Station-keeping of small amplitude motions around the collinear libration point in the real Earth-Moon system. Advances in Space Research,47(2011) 1127-1134.
[33]李国勇等,最优控制理论及参数优化.北京,国防工业出版社,2006.1
[34]Bookless J, Mclnnes C R. Control of Lagrange Point Orbits Using Solar Sail Propulsion, Acta astronautica,2008,62:159-176.
[35]Li H.M., Williams T., Reconfiguration of Sun-Earth libration point formations using solar radiation pressure [J]. Journal of Spacecraft and Rockets,2006,43(6):1328-1339.
[36]Williams T. W., Wang Z.S., Uses of solar radiation pressure for satellite formation flight [J]. International Journal of Robust and Nonlinear Control,2002,12(2-3):163-183.
[37]侯锡云,刘林,利用太阳帆定点探测器在地-月系共线平动点附近的探讨。宇航学报,2009,30(6)：2249-2257
[38]Gomez, G., Marcote, M., High-order analytical solutions of Hill's equations. Celest. Mech. Dyn.Astron.,94,197-211,2006.
[2]http://burro.astr.cwru.edu/stu/advanced/20th_soviet_mars.html
[3]http://burro.astr.cwru.edu/stu/advanced/20th_far_mariner.html
[4]Ulivi, Paolo, Harland, David M., Robotic Exploration of the Solar System Part I:The Golden Age 1957-1982, Praxis,2007
[5]http://www.astronautix.com/craft/marner34.htm
[6]http://www.astronautix.com/project/mars.htm
[7]http://zh.wikipedia.org/wiki/%E7%81%AB%E6%98%9F2%E5%8F%B7
[8]Harvey, Brian,Russian Planetary Exploration History, Development, Legacy and Prospects, 2007, Springer/Praxis
[9]ASIF A. SIDDIQI,Deep Space Chronicle-A Chronicle of Deep Space and Planetary Probes, Monographs in Aerospace History,2002.6
[10]http://zh.wikipedia.org/zh-cn/%E7%B6%AD%E4%BA%AC%E8%99%9F%E8%A8%88%E 5%8A%83
[11]http://nssdc.gsfc.nasa.gov/nmc/masterCatalog.do?sc=1975-075A
[12]http://zh.wikipedia.org/zh-cn/%E6%B5%B7%E7%9B%9C2%E8%99%9F
[13]http://nssdc.gsfc.nasa.gov/nmc/masterCatalog.do?sc=1975-083A
[14]http://en.wikipedia.org/wiki/Phobos_program
[15]http://www.hudong.com/wiki/%E7%81%AB%E6%98%9F%E8%A7%82%E5%AF%9F%E8 %80%85
[16]http://en.wikipedia.org/wiki/Mars_Observer
[17]http://en.wikipedia.org/wiki/Mars_Global_Surveyor
[18]http://nssdc.gsfc.nasa.gov/nmc/spacecraftOrbit.do?id= 1996-062A
[19]http://nssdc.gsfc.nasa.gov/planetary/text/mars96_timeline.txt
[20]http://en.wikipedia.org/wiki/Mars_96
[21]http://www.msss.com/mars/mars9x/mission.html
[22]http://mars.jpl.nasa.gov/MPF/mpf/mpfcruise.html
[23]http://burro.astr.cwru.edu/stu/advanced/20th_far_pathfinder.html
[24]http://en.wikipedia.org/wiki/Nozomi_(probe)
[25]http://www.astronautix.com/details/mar12378.htm
[26]http://en.wikipedia.org/wiki/Mars_Polar_Lander
[27]R.S.Saunders et.al.2001 Mars Odyssey Mission Summary, Space Science Reviews, Vol.110, N.O.1-2/2004.01.Available at website "http://www.springerlink.com/content/t4v8wvlwr 52265g2/"
[28]http://nssdc.gsfc.nasa.gov/nmc/masterCatalog.do?sc=2003-022A
[29]http://sci.esa.int/science-e/www/object/index.cfm?fobjectid=31037
[30]http://zh.wikipedia.org/wiki/%E5%8B%87%E6%B0%94%E5%8F%B7
[31]http://nssdc.gsfc.nasa.gov/nmc/masterCatalog.do?sc=2003-027A
[32]Mars Exploration Rover Launches,Press Kit,2003.06
[33]http://nssdc.gsfc.nasa.gov/nmc/masterCatalog.do?sc=2003-032A
[34]http://nssdc.gsfc.nasa.gov/nmc/masterCatalog.do?sc=2005-029A
[35]http://en.wikipedia.org/wiki/Phoenix_(spacecraft)
[36]http://nssdc.gsfc.nasa.gov/nmc/masterCatalog.do?sc=2007-034A
[37]http://www.dmuller.net/phoenix/
[38]Emily Lakdawalla. Phobos-Grunt Failure Report Released. Planetary Society. Feb.6,2012 [2012-02-08].
[39]http://zh.wikipedia.org/wiki/%E7%A6%8F%E5%B8%83%E6%96%AF%EF%BC%8D%E5 %9C%9F%E5%A3%A4
[40]http://zh.wikipedia.org/wiki/%E8%90%A4%E7%81%AB%E4%B8%80%E5%8F%B7
[41]http://zh.w ikipedia.org/wiki/%E7%81%AB%E6%98%9F%E7%A7%91%E5%AD%A6%E5 %AE%9E%E9%AA%8C%E5%AE%A4
[42]胡寿村,刘林,火星探测飞行轨道综述,中国宇航学会第25届飞行器测控学术年会论文集,2010。
[43]http://solarsystem.nasa.gov/missions/profile.cfm?MCode=ISEEICE
[44]http://nssdc.gsfc.nasa.gov/nmc/spacecraftDisplay.do?id=1978-079A
[45]ICE Encounter Operations, N.Fanelli & D.Morris
[46]http://www.mentallandscape.com/V_Vega.htm
[47]http://en.wikipedia.org/wiki/Giotto_(spacecraft)
[48]http://zh.wikipedia.org/wiki/%E5%96%AC%E6%89%98%E8%99%9F
[49]http://en.wikipedia.org/wiki/Galileo_(spacecraft)
[50]http://zh.wikipedia.org/wiki/%E4%BC%BD%E5%88%A9%E7%95%A5%E5%8F%B7%E6 %8E%A2%E6%B5%8B%E5%99%A8
[51]NEAR Shoemaker Spacecraft Mission Operations, Mark E. Holdridge
[52]http://near.jhuapl.edu/NewMissionDesign/orbPlan0516.html
[53]Recovery of NEAR's Mission to Eros.
[54]http://www.bjp.org.cn/otherpage/eros/erosl.html
[55]http://zh.wikipedia.org/wiki/%E6%B7%B1%E7%A9%BA%E4%B8%80%E8%99%9F
[56]http://en.wikipedia.org/wiki/Deep_Space_1
[57]http://zh.wikipedia.org/wiki/%E6%98%9F%E5%B0%98%E5%8F%B7
[58]http://en.wikipedia.org/wiki/Stardust_(spacecraft)
[59]http://en.wikipedia.org/wiki/CONTOUR
[60]http://zh.wikipedia.org/wiki/%E9%9A%BC%E9%B8%9F%E5%8F%B7
[61]http://en.wikipedia.org/wiki/Hayabusa
[62]http://zh.wikipedia.org/wiki/%E8%8F%B2%E8%90%8A%E6%8E%A2%E6%B8%AC%E5 %99%A8
[63]http://en.wikipedia.org/wiki/Rosetta_(spacecraft)
[64]http://zh.wikipedia.org/wiki/%E6%B7%B1%E5%BA%A6%E6%92%9E%E5%87%BB%E5 %8F%B7
[65]http://en.wikipedia.org/wiki/Deep_Impact_(spacecraft)
[66]http://zh.wikipedia.org/wiki/%E6%9B%99%E5%85%89%E8%99%9F
[67]http://en.wikipedia.org/wiki/Dawn_(spacecraft)
[68]http://en.wikipedia.org/wiki/Cassini%E2%80%93Huygens
[69]http://zh.wikipedia.org/wiki/%E5%8D%A1%E8%A5%BF%E5%B0%BC-%E6%83%A0%E6 %9B%B4%E6%96%AF%E5%8F%B7
[70]http://en.wikipedia.org/wiki/New_Horizons
[71]http://zh.wikipedia.org/wiki/%E6%96%B0%E8%A6%96%E9%87%8E%E8%99%9F
[1]刘林,胡松杰,王歆.航天动力学引论[M].南京：南京大学出版社,2006.
[2]Archinal, B.A., A'Hearn, M.F., Bowell, E., et al., Report of the IAU working group on cartographic coordinates and rotational elements:2009. Celest. Mech. Dyn. Astron.2011, 109:101-135.
[3]刘林,赵玉晖,张巍等,火星卫星运动的坐标系附加摄动及相应坐标系的选择.天文学报,2010,51(4)：412-421.
[4]Liu Lin, Zhao Yu-hui, Zhang Wei, et al., Coordinate Additional Perturbations to Mars Orbiters and Choice of Corresponding Coordinate System. Chinese Astronomy and Astrophysics, 2011,35(2):188-198.
[1]Battin, R.H., An Introduction to the Mathematics and Methods of Astrodynamics, American Institute of Aeronautics and Astronautics, Inc. New York, New York.1987.
[2]Gooding, R.H., On the Solution of Lambert's Orbital Boundary-Value Problem. RAE Technical Report 88027,1988.
[3]张旭辉,刘竹生,火星探测器轨道设计与优化技术,导航与航天运载技术,第2期(总第294期)：15-23,2008.
[4]赵国强,宝音贺西,李俊峰,基于B平面的火星探测直接转移轨道设计方法,中国空间科学技术,第1期：1-7,2012年2月.
[5]高飞,火星探测直接转移轨道精确求解研究,空间科学学报,30(6)：519-523,2010.
[6]陈杨,赵国强,宝音贺西,李俊峰,精确动力学模型下的火星探测轨道设计,中国空间科学技术,第1期：8-15,2012年2月.
[7]高飞,火星探测直接转移轨道设计研究,航天控制,28(4)：48-53,2010年8月.
[8]李云飞,行星际探测器轨道设计。南京大学天文系,天体测量与天体力学硕士论文。
[9]Hanspeter Schaub and John L. Junkins, Analytical Mechanics of Aerospace Systems (Chap. 12). January 1,2002
[10]尚海滨,崔平远,栾恩杰,地球-火星的燃料最省小推力转移轨道的设计与优化.宇航学报,27(6),1168-1173,2006年11月.
[11]尚海滨,崔平远,栾恩杰,星际小推力转移轨道快速设计方法,航空学报,28(6)：1281-1286,2007年11月.
[12]任远,崔平远,栾恩杰,利用混合法进行地球-火星小推力轨道设计,哈尔滨工业大学学报,39(3)：359-362,2007年3月.
[13]张旭辉,刘竹生,火星探测最优小推力变轨,导弹与航天运载技术,第1期(总第299期)：1-6,2009.
[14]R. Bertrand, J. Bernussou, Electric transfer optimization for Mars sample return mission, Acta Astronautica, Vol.48, No.5-12, pp.651-660,2011.
[15]G. Mingotti, F. Topputo, F. Bernelli-Zazzera, Earth-Mars transfers with ballistic escape and low-thrust capture, Celest Mech Dyn Astr (2011) 110:169-188
[16]任远,星际探测中的小推力转移轨道设计与优化方法研究,哈尔滨工业大学工学博士论文,2007年7月.
[17]李国勇等,最优控制理论及参数优化[M].北京,国防工业出版社,2006.1.
[1]Kozai Y., The motion of a close earth satellite. Astron. J.,1959,64(9):367-377
[2]Cook G. E., Basic theory for prod, a program for computing the development of satellite orbits. Celest. Mech,1973,7(3):301-314
[3]刘林,人造地球卫星轨道力学。高等教育出版社,1992.8。
[4]刘林,人造地球卫星在临界角附近运动的解。天文学报,1974,15(2)：230-240
[5]Liu Lin, A solution of the motion of an artificial satellite in the vicinity of the critical inclination. Chinese Astronomy,1977, 1(1):31-42.
[6]刘林,朱文耀,黄珹,人卫运动理论及其应用(Ⅰ)。天文学进展,1988,6(1)：42-51
[7]刘林,赵德滋,人造地球卫星运动中的共振问题。南京大学学报(自然科学版),1980,3：56-62
[8]张巍,刘林,关于地球飞行运动中的坐标系附加摄动问题。飞行器测控学报,2003,22(2)：25-29
[9]汤靖师,刘林,近地卫星运动的坐标系附加摄动在拟平均根数法中的处理。天文学报,2010.1,51(1)
[10]Jing-shi Tang, Lin Liu, The Application of Quasi-Mean-Element-Method to LEO under Additional Perturbation due to Change of Coordinate System. Chinese Astronomy and Astrophysics,2010,34(4):424-433.
[11]马剑波,刘林,王歆,地球非球形引力位中田谐项摄动的有关问题。天文学报,2001.11,42(4)
[12]Jian-bo Ma, Lin Liu, Xin Wang, Problems concerning the perturbation due to the tesseral harmonic terms in the nonspherical gravitational potential of the earth. Chinese Astronomy and Astrophysics,2002,26(2):235-244.
[13]刘林,王家松,月球卫星轨道变化的分析解。天文学报,39(1),1998.2
[14]Lin Liu, Jia-song Wang, An analytic solution of the orbital variation of lunar satellites. Chinese Astronomy and Astrophysics,1998,22(3):328-351.
[15]刘林,王歆,月球探测器轨道力学。国防工业出版社,2006.9
[16]刘林,C. K. Shum,在非球形引力摄动下金星轨道器运动的分析解。中国科学(A),29(10)：952-960,1999.10
[17]章圣泮,刘林,土卫七的运动理论。天文学报,23(2),1982.6
[18]Zhang Sheng-pan, Liu Lin, Theory of motion of hyperion. Chinese Astronomy and Astrophysics,1982,6(3):233-242.
[19]张伟,刘林,关于土卫八运动的轨道解。紫金山天文台台刊,18(1),1999-3
[20]刘世元,刘春保,刘林,卫星轨道变化规律的综合分析。飞行器测控学报,24(3),2005.6
[21]刘林,王歆,月球卫星轨道力学综述。天文学进展,21(4),2003.12
[22]王歆,刘林,制约卫星轨道寿命的另一种机制。天文学报,43(2),2002.5
[23]Xin Wang, Lin Liu, Another mechanism of restricting the lifetime of orbiting satellites. Chinese Astronomy and Astrophysics,2002,26(4):489-496.
[24]王歆,刘林,制约卫星轨道寿命的另一种机制(续)。天文学报,43(4),2002.11
[25]Xin Wang, Lin Liu, Another mechanism of restricting the lifetime of orbiting satellites (continued). Chinese Astronomy and Astrophysics,2003,27(1):107-113.
[26]王歆,刘林,目标天体极轨道卫星的轨道寿命。宇航学报,2001.9,22(5)
[27]刘林,王海红,关于月球低轨卫星运动的两个问题。天文学报,2006.7,47(3)
[28]Liu Lin, Wang Hai-hong, Two problems about the motion of low-moon-orbit satellites. Chinese Astronomy and Astrophysics,2006,30(4):437-446.
[29]刘林,汤靖师,火星轨道器运动的轨道变化特征。宇航学报,2008.3,29(2)
[30]刘林,王海红,胡松杰.人造地球卫星精密定轨(研究生用教材).南京：南京大学天文系,2005.
[31]刘林,航天器轨道理论.北京：国防工业出版社,2000.
[32]刘林,胡松杰,王歆.航天动力学引论.南京：南京大学出版社,2006.
[33]刘林,赵玉晖,张巍等,火星卫星运动的坐标系附加摄动及相应坐标系的选择.天文学报,2010,51(4)：412-421.
[34]Liu Lin, Zhao Yu-hui, Zhang Wei, et al., Coordinate Additional Perturbations to Mars Orbiters and Choice of Corresponding Coordinate System. Chinese Astronomy and Astrophysics,2011,35(2):188-198.
[35]Fehlberg E, Classical Fifth-, Sixth-, Seventh-and Eig-hth Order Runge-Kutta Formulas with Stepsize Contr-ol, NASA TR R-287,1968.
[36]P. Kenneth Seidelmann, B. A. Archinal, M. F. A'hearn, et al. Report of the IAU/IAG Working Group on cartographic coordinates and rotational elements[J]:2006. Celestial Mech Dyn Astr (2007)98:155-180
[37]Jon. Giorgini. Horizons On-Line Ephemeris System[DB/OL]. (2010-01-15) [2010-07-14]. http://ssd.jpl.nasa.gov/horizons.cgi.
[1]http://ssd.jpl.nasa.gov/sbdb.cgi#top
[2]http://comets-asteroids.findthedata.org/1/15723/12711-Tukmit-1991-BB
[3]http://ssd.jpl.nasa.gov/sbdb.cgi?sstr=99942;orb=0;cov=1;log=0;cad=0#elem
[4]http://neo.jpl.nasa.gov/risk/a99942.html
[5]http://ssd.jpl.nasa.gov/sbdb.cgi?sstr=1996fg3;orb=0;cov=1;log=0;cad=0#elem
[6]http://www.johnstonsarchive.net/astro/astmoons/am-175706.html
[7]Gooding, R.H. On the Solution of Lambert's Orbital Boundary-Value Problem. RAE Technical Report 88027,1988
[8]李国勇等,最优控制理论及参数优化[M].北京,国防工业出版社,2006.1.
[9]任远,星际探测中的小推力转移轨道设计与优化方法研究,哈尔滨工业大学工学博士论文,2007年7月.
[10]任远,崔平远,栾恩杰.基于标称轨道的小推力轨道设计方法.吉林大学学报(工学版),2006,36(6)：998-1002.
[1]Szebehely, V. Theory of Orbits. Academic Press, New York and London,1967
[2]刘林,胡松杰,王歆.航天动力学引论.南京：南京大学出版社,2006
[3]Gomez, G., Jorba, A., Masdemont, J., Simo, C.:Dynamics and Mission Design near Libration Point Orbits, Vol. Ⅲ, Advanced Methods for Collinear Points. World Scientific, Singapore (2001).
[4]Jorba A, Masdemont J., Dynamics in the centre manifold of the collinear points of the restricted three body problem, Physica D,132:189-213(1999).
[5]Richardson D.L.,1980, Analytic Construction of Periodic Orbits about the Collinear Points, Celestial Mechanics and Dynamical Astronomy, Vol 22,241-253
[6]Farquhar R. W., The Moon's influence on the location of the Sun-Earth exterior libration point, Celestial Mechanics,2:131-133,1970.
[7]Richardson D.L. and Cary N. D., A uniformly valid solution for motion about the interior libration point of the perturbed elliptic-restricted problem. In AAS/AIAA Astrodynamics Specialist Conference, AAS Paper 75-021,, July 1975.
[8]Farquhar R. W. and Kamel A. A., Quasi-periodic orbits about the translunar libration point, Celestial Mechanics,7:458-473,1973.
[9]Hou X.Y. and Liu L., On quasi-periodic motions around the triangular libration points of the real Earth-Moon system. Celestial Mechanics and Dynamical Astronomy, (2010) 108: 301-313.
[10]Hou X.Y. and Liu L., On quasi-periodic motions around the collinear libration points in the real Earth-Moon system. Celestial Mechanics and Dynamical Astronomy, (2011) 110:71-98.
[11]Gomez, G., Llibre J., Martinez R., and Simo, C.:Dynamics and Mission Design near Libration Point Orbits, Vol. I, Fundamentals:The Case of Collinear Libration Points. World Scientific, Singapore (2001).
[12]E. W. Brown and C. A. Shook. Planetary Theory. Dover,1964.
[13]Cheng A.F., Near Earth Asteroid Rendezvous:Mission Summary. Asteroids Ⅲ, W.F. Bottke Jr., A. Cellino, P. Paolicchi, and R. P. Binzel (eds), University of Arizona Press, Tucson, 351-366,2002.
[14]Thomas V.C., Makowski J.M., and Brown G.M. et al., The Dawn Spacecraft. Space Science Reviews, Volume 163, Issue 1-4,175-249,2011.
[15]Yoshikawa Makoto, Fujiwara Akira, Kawaguchi Jun'ichiro, Hayabusa and its adventure around the tiny asteroid Itokawa. Highlights of Astronomy, Volume 14,323-324,2007.
[16]Richardson D. L., Halo Orbit Formulation for the ISEE-3 Mission. Journal of Guidance and Control, Vol.3, No.6,1980, pp.543-548.
[17]Folda D., Vaughn F., A survey of Earth-Moon libration orbits:stationkeeping strategies and intra-orbit transfers. In:AIAA 2004-4741, AIAA/AAS Astrodynamics Specilist Conference, Providence, Rhode Island,2004.
[18]Kim M.,2001, Periodic Spacecraft Orbits for Future Space-Based Deep Space Observations Technique Report., Vienna Institute of Technology, Vienna, Astria
[19]G6mez G, Masdemont J. and Sim6 C, Quasi-Halo Orbits Associated with Libration Points. Journal of Astronautics Science,42(2):135-176(1998).
[20]Howell K.C. and Pernicka H.J., Numerical Determination of Lissajous Trajectories in the Restricted Three-Body Problem, Celestial Mechanics and Dynamical Astronomy,41: 107-124(1987).
[21]Morrison D.D., Riley J.D. and Zancanzro J.F., Multiple Shooting Method for Two-Point Boundary Value Problem, Communications of the ACM,5,12,613-614(1962).
[22]侯锡云,博士毕业论文.南京大学,2008
[23]Liu Lin, Wang Haihong, Ma Jianbo, On the Formation Flying of Satellite Constellations. Chin. Astro. Astrophy.,2004,28(2):188-199.
[24]刘林,侯锡云,轨道力学(研究生用教材),南京大学天文学系,2007.08
[25]Farquhar R.W., The control and use of libration point satellites. Technical Report TR R346, NASA,1970.
[26]Breakwell, J.V., Kamel, A.A., and Ratner M.J., Station-keeping for a translunar communications station. Celestial Mechanics,10(3):357-373,1974.
[27]Howell K.C, Pernicka H.J. Stationkeeping method for libration point trajectories. J. Guid. Control Dynam.16(1):151-159,1993.
[28]Gomez G., Howell K., Masdemont J., et al. Station-keeping strategies for translunar libration point orbits. Adv. Astronaut. Sci.99:949-967,1998.
[29]Anderson R.L., Lo M.W., Born G.H. Application of local Lyapunov exponents to maneuver design and navigation in the three-body problem, in:AAS 03-569, AIAA/AAS Astrodynamics Specialist Conf., Big Sky, Montana, USA, Aug 3-7,2003.
[30]Folta D., Vaughn F. A survey of Earth-Moon libration orbits:stationkeeping strategies and intra-orbit Transfers, in:AIAA 2004-4741, AIAA/AAS Astrodynamics Specialist Conf., Providence, Rhode Island, USA, Aug 16-19,2004.
[31]Kulkarni J.E., Campbell M.E., Dullerud G.E. Stabilization of spacecraft flight in halo orbits: an H∞ approach. IEEE. Trans. Control Syst. Technol.14(3):572-578,2006.
[32]Hou X.Y. and Liu L., Station-keeping of small amplitude motions around the collinear libration point in the real Earth-Moon system. Advances in Space Research,47(2011) 1127-1134.
[33]李国勇等,最优控制理论及参数优化.北京,国防工业出版社,2006.1
[34]Bookless J, Mclnnes C R. Control of Lagrange Point Orbits Using Solar Sail Propulsion, Acta astronautica,2008,62:159-176.
[35]Li H.M., Williams T., Reconfiguration of Sun-Earth libration point formations using solar radiation pressure [J]. Journal of Spacecraft and Rockets,2006,43(6):1328-1339.
[36]Williams T. W., Wang Z.S., Uses of solar radiation pressure for satellite formation flight [J]. International Journal of Robust and Nonlinear Control,2002,12(2-3):163-183.
[37]侯锡云,刘林,利用太阳帆定点探测器在地-月系共线平动点附近的探讨。宇航学报,2009,30(6)：2249-2257
[38]Gomez, G., Marcote, M., High-order analytical solutions of Hill's equations. Celest. Mech. Dyn.Astron.,94,197-211,2006.