堆叠式卫星系统分离动力学关键技术与展望

  • 金栋平 ,
  • 丁鼎峰 ,
  • 文浩 ,
  • 张晓彤 ,
  • 孙加亮
展开
  • 1. 南京航空航天大学
    2.
    3. 上海卫星工程研究所

收稿日期: 2024-10-08

  修回日期: 2024-10-29

  网络出版日期: 2024-10-29

基金资助

国家自然科学基金;民用航天预研项目

Key technologies and prospects for separation dynamics of stacked satellite systems

  • JIN Dong-Ping ,
  • DING Ding-Feng ,
  • WEN Hao ,
  • ZHANG Xiao-Tong ,
  • SUN Jia-Liang
Expand

Received date: 2024-10-08

  Revised date: 2024-10-29

  Online published: 2024-10-29

摘要

组建低轨卫星互联网星座用于通信,需要多星在轨互联,如何高效率地构建在轨星座并成功组网是一项复杂的系统工程问题。目前,普遍采用堆叠式一箭多星发射入轨,继而在轨自主分离的方式进行组网。为此,本文综述了堆叠式卫星的应用需求与发射优势,梳理了国内外堆叠式卫星的发射情况。针对堆叠式卫星在轨分离技术难点,概述了堆叠式卫星构型设计及锁紧分离机构设计优化;针对堆叠式卫星分离动力学问题,总结了分离前堆叠卫星组合体的动力学建模及分析方法、分离过程多刚体系统动力学建模与仿真手段,以及分离过程接触碰撞的检测算法;针对堆叠式卫星分离过程地面物理仿真问题,介绍了堆叠式卫星同层分离与层间分离地面实验方法。最后,总结了堆叠式卫星分离动力学关键技术,并指出若干值得深入研究的前沿方向。

本文引用格式

金栋平 , 丁鼎峰 , 文浩 , 张晓彤 , 孙加亮 . 堆叠式卫星系统分离动力学关键技术与展望[J]. 航空学报, 0 : 0 -0 . DOI: 10.7527/S1000-6893.2024.31342

Abstract

Recent years have witnessed the rapid development of satellite internet constellation via low-orbit communication satellites in the main aerospace industries of various countries. For efficient construction of the satellite internet constellation, researchers from the main aerospace industries focus on the technologies of multi-satellite launch of stacked satellite system, as well as autonomous sepa-ration and reconfiguration on orbit. Therefore, this paper reviews the application requirements and launch merits of stacked satellites, and introduces the developments of the launched stacked satellites all over the world. For the challenges of on orbit separation, this paper also presents the configuration design of the stacked satellites and the optimization design of separation mechanisms. For the separation dynamics of the stacked satellites, the paper outlines the dynamic modeling and simulation methods for the system before separation, the rigid multibody system during separation, and most importantly the contact detection algorithms during separation. For the ground experiment validations, the paper briefly exhibits the experiment platform and results for separations of two satellites between layers and in the same layer. Finally, the paper summarizes the key technologies for separation dynamics of stacked satellites and points out several prospects for further study.

参考文献

[1] 谢涛, 余东峰, 李云鹏, 等. 星链与星舰启示和我国商业航天探索[J]. 卫星应用, 2023(05): 45-50.
XIE T, YU D F, LI Y P, et al. Inspiration from Starlink and Starship and China's commercial space exploration[J]. Satellite Application, 2023(05): 45-50 (in Chinese).
[2] 袁浚. 低轨卫星互联网研究与应用展望[J]. 广播与电视技术, 2022, 49(11): 33-35.
YUAN J. Research and application prospect of low-orbit satellite Internet [J]. Radio & TV Broadcast Engineering, 2022, 49(11): 33-35 (in Chinese).
[3] 张更新, 王运峰, 丁晓进, 等. 卫星互联网若干关键技术研究[J]. 通信学报, 2021, 42(08): 1-14.
ZHANG G X, WANG Y F, DING X J, et al. Research on several key technologies of satellite Internet[J]. Journal on Communications. 2021, 42(08): 1-14 (in Chinese).
[4] 蒋瑞红, 冯一哲, 孙耀华, 等. 面向低轨卫星网络的组网关键技术综述[J]. 电信科学, 2023, 39(02): 37-47.
JIANG R H, FENG Y Z, SUN Y H, et al. A survey on networking key technologies for LEO satellite network[J]. Telecommunications Science. 2023, 39(02): 37-47 (in Chinese).
[5] 张鑫伟, 付郁. 2020年全球航天发射统计分析[J]. 国际太空, 2021(02): 18-23.
ZHANG X W, FU Y. Statistical analysis of global space launches in 2020[J]. Space International, 2021(02): 18-23 (in Chinese).
[6] 陈牧野, 牟宇, 周宁, 等. “星链”堆叠式卫星连接与分离技术及应用[J]. 国际太空, 2022(04): 24-28.
CHEN M Y, MOU Y, ZHOU N, et al. Technology and application of "Star Link" stackable satellite connection and separation[J]. 2022(04): 24-28 (in Chinese).
[7] 王峰, 叶水驰, 曹喜滨. 一箭多星发展现状综述及核心技术分析[C]//中国空间科学学会. 中国空间科学学会2013年空间光学与机电技术研讨会会议论文集. 西安: 中国空间科学学会, 2013: 6.
WANG F, YE S C, CAO X B. Summary of development status and core technology analysis of multiple satellites with one arrow[C]// Chinese Society of Space Science. Proceedings of the 2013 Symposium on Space Optics and Mechatronics of the Chinese Society of Space Science. Xi'an: Chinese Society of Space Science, 2013: 6 (in Chi-nese).
[8] 张兵, 岑拯. 多星分离的ADAMS仿真[J]. 导弹与航天运载技术, 2004(02): 1-6.
ZHANG B, CEN Z. The ADAMS simulation of multi-satellite separation system[J]. Missile and Space Launch Vehicles, 2004(02): 1-6 (in Chinese).
[9] 丁继锋. 星箭分离缓冲设计方法及试验验证研究[J]. 强度与环境, 2016, 43(02): 17-24.
DING J F. Shock isolation of satellite-rocket separation and its test verification[J]. Strength & Environment Engi-neering, 2016, 43(02): 17-24 (in Chinese).
[10] 王金昌, 闫波, 张佳, 等. 基于虚拟样机的多星分离仿真分析[J]. 中国空间科学技术, 2016, 36(06): 70-76.
WANG J C, YAN B, ZHANG J, et al. Multi-satellite sep-aration simulation analysis based on virtual prototype[J]. Chinese Space Science and Technology, 2016, 36(06): 70-76 (in Chinese).
[11] 李烁, 刘焱, 胡冬生, 等. 国外微纳运载火箭发展现状及趋势分析[J]. 中国航天, 2020(02): 38-42.
LI S, LIU Y, HU D S, et al. Development status and trend analysis of micro-nano launch vehicles in foreign coun-tries[J]. Aerospace China, 2020(02): 38-42 (in Chinese).
[12] 刘悦.“下一代铱星”系统首批10颗卫星成功发射[J]. 国际太空, 2017(04): 52-54.
LIU Y. The first 10 satellites of Iridium NEXT launched successfully[J]. Space International, 2017(04): 52-54 (in Chinese).
[13] 王羽, 李清, 李克军, 等. Starlink星座应用现状及分析[J]. 天地一体化信息网络, 2023, 4(02): 93-102.
WANG Y, LI Q, LI K J, et al. Application status and analysis of Starlink constellation[J]. Space-Integrated-Ground Information Network, 2023, 4(02): 93-102 (in Chinese).
[14] 付郁, 张继荣. 2022年全球航天发射统计分析[J]. 国际太空, 2023(02): 6-12.
FU Y, ZHANG J R. Statistical analysis of global space launches in 2022[J]. Space International, 2023(02): 6-12 (in Chinese).
[15] 张炎, 宋战锋. 英国“天网”军用通信卫星系统[J]. 国际太空, 2009(01): 14-20.
ZHANG Y, SONG Z F. British Skynet military commu-nication satellite system [J]. Space International, 2009(01): 14-20 (in Chinese).
[16] 龚宇鹏. 低轨巨型星座构型设计及覆盖分析方法研究[D]. 哈尔滨工业大学, 2022.
GONG Y P. Research on configuration design and cover-age analysis method of low orbit giant constellation[D]. Harbin Institute of Technology, 2022 (in Chinese).
[17] 王存恩. 日本“一箭多星”发射现状及典型实例分析[J]. 国际太空, 2015(10): 23-28.
WANG C E. Case study of Japan's multi-payload launch[J]. Space International, 2015(10): 23-28 (in Chi-nese).
[18] 刘进军. 多星发射与世界航天纪录[J]. 卫星电视与宽带多媒体, 2013(12): 18-22.
LIU J J. Multi-satellite launch and World Space Record[J]. Satellite TV & IP Multimedia, 2013(12): 18-22 (in Chi-nese).
[19] 黄志澄. 印度太空力量的新发展[J]. 国际太空, 2021(01): 52-58.
HUANG Z C. New development of Indian space force[J]. Space International, 2021(01): 52-58 (in Chinese).
[20] 兰顺正. 中国航天再破记录, “一箭多星”技术更上一层楼[J]. 世界知识, 2023(14): 72-73.
LAN S Z. China's space has broken another record, and the "one arrow and multiple stars" technology has reached a new level[J]. World Affairs, 2023(14): 72-73 (in Chi-nese).
[21] 黄志澄. 长征-6运载火箭开启我国航天新“长征”[J]. 国际太空, 2015(10): 34-35.
HUANG Z C. CZ-6 rocket starts China's new long march[J]. Space International, 2015(10): 34-35 (in Chi-nese).
[22] 孙洪雨, 李小明, 柳萌. “一箭41星”发射的关键要素分析[J]. 国际太空, 2024(03): 47-52.
SUN H Y, LI X M, LIU M. Analysis of key elements for the launch of "One Arrow and 41 Stars" [J]. Space Inter-national, 2024(03): 47-52 (in Chinese).
[23] 柏亮. 卫星互联网的技术体系、发展趋势与应用[J]. 通信电源技术, 2020, 37(07): 181-183.
BAI L. Technology system and development trend and application of satellite Internet[J]. Telecom Power Tech-nology, 2020, 37(07): 181-183 (in Chinese).
[24] 朱剑涛, 林益明. 适合于“一箭多星”发射的卫星构型特点综述[J]. 国际太空, 2007(06): 23-29.
ZHU J T, LIN Y M. A review of the configuration charac-teristics of satellites suitable for multi-satellite launch[J]. Space International, 2007(06): 23-29 (in Chinese).
[25] 姚延风, 裴胜伟, 李东泽, 等. “一箭多星”发射低地球轨道卫星的构型优化设计方法[J]. 航天器工程, 2016, 25(03): 32-39.
YAO Y F, PEI S W, LI D Z, et al. Configuration optimiza-tion design method of LEO satellite of multi-satellite launch[J]. Spacecraft Engineering, 2016, 25(03): 32-39 (in Chinese).
[26] 吴胜宝, 胡冬生. 国外“一箭多星”发射现状及关键技术分析[J]. 国际太空, 2015(10): 18-22.
WU S B, HU D S. Current situation and key technology of multi-payload launch missions[J]. Space International, 2015(10): 18-22 (in Chinese).
[27] 杨谋祥, 郝芳. 航天火工装置[J]. 航天返回与遥感, 1999(04): 37-40.
YANG M X, HAO F. Space pyrotechnics devices [J]. Spacecraft Recovery & Remote Sensing, 1999(04): 37-40 (in Chinese).
[28] 王军评, 毛勇建, 黄含军. 点式火工分离装置冲击载荷作用机制的数值模拟研究[J]. 振动与冲击, 2013, 32(02): 9-13+32.
WANG J P, MAO Y J, HUANG H J. Numerical simula-tion for impulsively loading mechanism of a point pyro-technic separation device[J]. Journal of Vibration and Shock, 2013, 32(02): 9-13+32 (in Chinese).
[29] 温洋. 某航天火工装置可靠性分析与评估方法研究[D]. 北京理工大学, 2015.
WEN Y. Research on reliability analysis and evaluation method of an aerospace pyrotechnics device[D]. Beijing Institute of Technology, 2015 (in Chinese).
[30] 高庆, 陈新民, 赵永辉. 线式分离结构高应力释放对高频冲击环境的影响分析[J]. 振动与冲击, 2016, 35(21): 166-170.
GAO Q, CHEN X M, ZHAO Y H. Effect of high stress release on high frequency shock environment of linear separation structure [J]. Journal of Vibration and Shock, 2016, 35(21): 166-170 (in Chinese).
[31] 冯丽娜, 李东, 田建东, 等. 基于变形圆筒实验的扁平管组件能量输出效率研究[J]. 振动与冲击, 2020, 39(23): 176-181.
Feng L N, Li D, Tian J D, et al. Simulation and tests for expansion performance of a flat tube[J]. Journal of Vibra-tion and Shock, 2020, 39(23): 176-181 (in Chinese).
[32] 王军评, 毛勇建, 吕剑, 等. 爆炸螺栓冲击响应的主要影响因素研究[J]. 振动与冲击, 2019, 38(13): 42-49.
WANG J P, Main influence factors on pyrotechnic-shock response of explosive bolts[J]. Journal of Vibration and Shock, 2019, 38(13): 42-49 (in Chinese).
[33] 唐科, 胡振兴, 曲展龙, 等. 典型航天火工装置降冲击技术研究[J]. 宇航总体技术, 2022, 6(05): 1-9.
TANG K, HU Z X, QU Z L, et al. Research on shock re-duction technology of typical aerospace explosive devic-es[J]. Astronautical Systems Engineering Technology, 2022, 6(05): 1-9 (in Chinese).
[34] 唐科, 汪锐琼, 曲展龙, 等. 温度-湿度-高度环境对航天火工装置性能的影响[J]. 装备环境工程, 2022, 19(02): 7-13.
TANG K, WANG R Q, QU Z L, et al. Influence of tem-perature-humidity-altitude environment on the perfor-mance of aerospace explosive devices[J]. Equipment En-vironmental Engineering, 2022, 19(02): 7-13 (in Chinese).
[35] LUNA A. Operational improvements of a pyrotechnic ultra low shock separation nut[C]//Proceedings of the 36th Aerospace Mechanisms Symposium. 2002: 131-136.
[36] 仲作阳, 张海联, 周建平, 等. 航天器非火工连接分离技术研究综述[J]. 载人航天, 2019, 25(1): 128-142.
ZHONG Z Y, ZHANG H L, ZHOU J P, et al. Review of non-pyrotechnic connection and separation technology of spacecraft[J]. Manned Spaceflight, 2019, 25(1): 128-142 (in Chinese).
[37] 白志富, 果琳丽, 陈岱松. 新型非火工星箭连接分离技术[J]. 导弹与航天运载技术, 2009(01): 31-37.
BAI Z F, GUO L L, CHEN D S. Late-model non-pyrotechnic devices for separation of satellite-launching vehicle[J]. Missiles and Space Vehicles, 2009(01): 31-37 (in Chinese).
[38] CHAPUT D, VISCONTI M, EDWARDS M. Payload hold-down and release mechanisms[C//28th Aerospace Mechanisms Symposium, 1994: 395-411.
[39] 赵正阳, 苌群峰, 冯萃峰, 等. 微纳卫星聚合体分体式锁紧分离方案研究与验证[J]. 机械设计, 2023, 40(S2): 109-113.
ZHAO Z Y, CHANG Q F, Feng C F, et al. Research and verification of split locking separation scheme for micro-nano-satellite polymers[J]. Journal of Machine Design, 2023, 40(S2): 109-113 (in Chinese).
[40] Separation Systems Rocket Lab[EB/OL]. [2024-09-20]. https://www.rocketlabusa.com/space-systems/separation-systems/.
[41] YOO Y I, JEONG J W, LIM J H, et al. Development of a non-explosive release actuator using shape memory alloy wire[J]. Review of scientific instruments, 2013, 84(1): 015005.
[42] LUCY M, HARDY R, KIST E. Report on alternative devices to pyrotechnics on spacecraft[C]//10th Annual AIAA /USU Conference on Small Satellites, 1996: 1-19.
[43] VáZQUEZ J, BUENO I. Non explosive low shock reus-able 20 kN hold-down release actuator[C]//9th European space mechanisms and tribology symposium. 2001, 480: 131-135.
[44] WEBSTER R G. No-shock separation mechanism: U.S. Patent 5,248,233[P]. 1993-9-28.
[45] GALL K, LAKE M, HARVEY J, ET AL. Development of a shockless thermally actuated release nut using elastic memory composite material [C] // 44th AIAA/ASME/ASCE/AHS/ASC Structures, Structur-al Dynamics, and Materials Conference. 2003: 1582.
[46] 胡晓楠, 吴君, 彭金圣, 等. 基于记忆合金的大承载低冲击解锁机构设计与试验研究[J]. 科学技术与工程, 2016, 16(30): 319-323.
HU X N, WU J, PENG J S, et al. Design and experi-mental research of a large load and low shock release de-vice on shape memory alloy[J]. Science Technology and Engineering, 2016, 16(30): 319-323 (in Chinese).
[47] 崔垚. 航天器低冲击分离控制技术研究[D]. 哈尔滨工业大学, 2014.
YAO C. Research on low impact separation control tech-nology of spacecraft[D]. Harbin Institute of Technology, 2014 (in Chinese).
[48] TUSZYNSKI A. Alternatives to pyrotechnics-nitinol release mechanisms[C]//Proceedings of the 36th Aero-space Mechanisms Symposium. 2002: 137-139.
[49] LEE M, JO J, TAK W, et al. Shape memory alloy (SMA) based non-explosive separation actuator (NEA) with a re-dundant function[J]. International Journal of Precision Engineering and Manufacturing, 2011, 12: 569-572.
[50] TAK W, LEE M, KIM B. Ultimate load and release time controllable non-explosive separation device using a shape memory alloy actuator[J]. Journal of Mechanical Science and Technology, 2011, 25: 1141-1147.
[51] BUSCH J D, BOKAIE M D. Implementation of heaters on thermally actuated spacecraft mechanisms[C]//NASA. Lewis Research Center, The 28th Aerospace Mechanisms Symposium. 1994.
[52] LEES J, SCHAEFER E. Design and testing of the CRISP tracking mirror cover and release mecha-nism[C]//Proceeding of the 36th Aerospace Mechanisms Symposium, Glenn Research Center. 2002: 63-76.
[53] PURDY W. The clementine mechanisms william purdy and michael hurley[C]//The 29th Aerospace Mechanisms Symposium. NASA, 1995: 109.
[54] CREMERS J, GOOIJER E, KESTER G. SPECIAL FUNCTIONS: Multipurpose hold down and release mechanism (MHRM) [C]//8th European Space Mecha-nisms and Tribology Symposium. 1999, 438: 329.
[55] STEWART A, BRODEUR S J. A new and innovative use of the thermal knife and Kevlar cord components in a re-straint and release system[C]// 9th European Space Mech-anisms and Tribology Symposium, 2001: 231-238.
[56] 蔡逢春, 孟宪红. 用于连接与分离的非火工装置[J]. 航天返回与遥感, 2005, 26(4): 50-55.
CAI F C, MENG X H. Non-pyrotechnic device for join-ing and separating[J], Spacecraft Recovery & Remote Sensing, 2005, 26(4): 50-55 (in Chinese).
[57] LAN W, BROWN J, TOORIAN A, et al. CubeSat devel-opment in education and into industry[M]//Space 2006. 2006: 7296.
[58] TOORIAN A, BLUNDELL E, PUIG-SUARI J, et al. CubeSats as responsive satellites[M]//Space 2005. 2005: 6828.
[59] 尚立斌, 王安平, 王珂, 等. 基于液态金属的锁紧/解锁装置在空间展开机构中的应用[J]. 载人航天, 2017, 23(04): 572-576.
SHANG L B, WANG A P, WANG K, et al. Application of locking/unlocking device based on liquid metal in space deployable mechanism[J]. Manned Space-flight, 2017, 23(04): 572-576 (in Chinese).
[60] 陈靖, 张翔, 陈卫东, 等. 微小卫星解锁分离装置主结构设计分析及优化[J]. 航天器环境工程, 2012, 29(06): 681-686.
CHEN J, ZHANG X, CHEN W D, et al. Main structural design analysis and optimization of connection and sepa-ration mechanism of minisatellite[J]. Spacecraft Environ-ment Engineering, 2012, 29(06): 681-686 (in Chinese).
[61] 杜正刚, 娄路亮, 张立强, 等. 冷气分离装置设计参数对冲量的影响[J]. 导弹与航天运载技术, 2011(04): 1-3.
DU Z G, LOU L L, ZHANG L Q, et al. Effect of cold-gas separating device design parameters on impulse[J]. Missiles and Space Launch Vehicles, 2011(04): 1-3 (in Chinese).
[62] 陈金宝, 霍伟航, 陈传志, 等. 堆叠式多星分离动力学研究[J]. 机械制造与自动化, 2023, 52(02): 7-10.
CHENG J B, HUO W H, CHEN C Z, et al. Dynamic analysis of stacked multi-satellite separation[J]. Machine Building & Automation, 2023, 52(02): 7-10 (in Chinese).
[63] 姜周, 卢松涛, 吕鹏伟, 等. 一种多星分离的姿控联合仿真方法[J]. 宇航总体技术, 2024, 8(02): 59-65.
JIANG Z, LU S T, LV P W, et al. A joint simulation meth-od for multi-satellite separation with attitude control[J]. Astronautical Systems Engineering Technology, 2024, 8(02): 59-65 (in Chinese).
[64] LILOV L, LORER M. Dynamic analysis of multi-rigid‐body system based on the Gauss principle[J]. ZAMM‐Journal of Applied Mathematics and Mechan-ics/Zeitschrift für Angewandte Mathematik und Mechanik, 1982, 62(10): 539-545.
[65] HAUG E J. Computer aided kinematics and dynamics of mechanical systems[M]. Allyn and Bacon Boston, 1989.
[66] 孙加亮, 张晓亮, 金栋平. 堆叠卫星的分离与重构动力学研究[J]. 应用数学和力学, 2024, 45(1): 1-11.
SUN J L, ZHANG X L, JIN D P. Separation and recon-figuration dynamics of stacked satellites[J]. Applied Mathematics and Mechanics, 2024, 45(1): 1-11 (in Chi-nese).
[67] Zhang X, Sun J, Jin D, et al. Dynamics of reconfiguration and assembly of a stacked satellite system[J]. Acta Astro-nautica, 2024, 218: 367-382.
[68] 罗操群, 孙加亮, 文浩, 等. 多刚体系统分离策略及释放动力学研究[J]. 力学学报, 2020, 52(02): 503-513.
LUO C Q, SUN J L, WEN H, et al. Research on separa-tion strategy and deployment dynamics of a space multi-rigid-body system[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(02): 503-513 (in Chinese).
[69] SUN J, TAN S, WEN H, et al. Contact-free release dy-namics of tens of stacked satellites with multiaxial rota-tions[J]. Advances in Space Research, 2023, 71(1): 492-506.
[70] LUO C, SUN J, WEN H, et al. Autonomous separation deployment dynamics of a space multi-rigid-body system with uncertain parameters[J]. Mechanism and Machine Theory, 2023, 180: 105175.
[71] LEE T, MCCLAMROCH N H, LEOK M. A Lie group variational integrator for the attitude dynamics of a rigid body with applications to the 3D pendu-lum[C]//Proceedings of 2005 IEEE Conference on Con-trol Applications, 2005. CCA 2005. IEEE, 2005: 962-967.
[72] NORDKVIST N, SANYAL A K. A Lie group variational integrator for rigid body motion in SE (3) with applica-tions to underwater vehicle dynamics[C]//49th IEEE con-ference on decision and control (CDC). IEEE, 2010: 5414-5419.
[73] 丁希仑, 刘颖. 用李群李代数分析具有空间柔性变形杆件的机器人动力学[J]. 机械工程学报, 2007, 43(12): 184-189.
DING X L, LIU Y. Dynamics analysis of robot with spa-tial compliant links using Lie Group and Lie algebra[J]. Journal of Mechanical Engineering, 2007, 43(12): 184-189 (in Chinese).
[74] 白龙, 董志峰, 戈新生. 基于 Lie 群的刚体动力学建模及数值计算方法研究[J]. 应用数学和力学, 2015, 36(8): 833-843.
BAI L, DONG Z F, GE X S. Lie Group and Lie Algebra modeling for numerical calculation of rigid body dynam-ics[J]. Applied Mathematics and Mechanics, 2015, 36(8): 833-843 (in Chinese).
[75] 张继锋, 邓子辰, 张凯. 结构动力方程求解的改进精细Runge-Kutta方法[J]. 应用数学和力学, 2015, 36(4): 378-385.
ZHANG J F, DENG Z C, ZHANG K. An improved pre-cise Runge-Kutta method for structural dynamic equa-tions[J]. Applied Mathematics and Mechanics, 2015, 36(4): 378-385 (in Chinese).
[76] 黄子恒, 陈菊, 张志娟, 等. 多刚体动力学仿真的李群变分积分算法[J]. 动力学与控制学报, 2022, 20(1): 8-17.
HUANG Z H, CHEN J, ZHANG Z J, et al. Lie Group Variational integration for multi-rigid body system dynam-ics simulation[J]. Journal of Dynamics and Control, 2022, 20(1): 8-17 (in Chinese).
[77] 田龙飞, 李华, 刘武, 等. 基于重要性测度的一箭多星分离安全性分析[J]. 中国科学: 技术科学, 2019, 49(7): 803-814.
TIAN L F, LI H, LIU W, et al. Study on safety of multi-satellite launch mission based on importance measure[J]. Scientia Sinica (Technologica), 2019, 49(7): 803-814 (in Chinese).
[78] 杨慧, 周静, 马利. 一箭多星发射飞行间距预示方法研究[J]. 航天器工程, 2017, 12: 39.
YANG H, ZHOU J, MA L. Study on prediction of spac-ing between satellites in the multi-satellite launch mis-sions[J]. Spacecraft Engineering, 2017, 12:39 (in Chi-nese).
[79] BRIDGES C P, SAUTER L, PALMER P. Formation deployment & separation simulation of multi-satellite Sce-narios using SatLauncher[C]//2011 Aerospace Conference. IEEE, 2011: 1-9.
[80] 张晓亮, 张晓彤, 刘福寿, 等. 卫星在轨分离地面试验方案设计及动态仿真分析[J]. 上海航天(中英文), 2023, 40(02): 32-40.
ZHANG X L, ZHANG X T, LIU F S, et al. Ground ex-periment design and dynamic simulation analysis for sep-aration of in-orbit satellite[J]. Aerospace Shanghai (Chi-nese & English), 2023, 40(02): 32-40 (in Chinese).
[81] 张晓亮. 堆叠卫星分离与重构组装动力学研究[D]. 南京航空航天大学, 2024.
ZHANG X L. Dynamics of reconfiguration and assem-bly of a stacked satellites system[D]. Nanjing University of Aeronautics and Astronautics, 2024 (in Chinese).
文章导航

/