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空间刚性杆--弹簧组合结构轨道、姿态耦合动力学分析

尹婷婷, 邓子辰, 胡伟鹏, 李庆军, 曹珊珊

尹婷婷, 邓子辰, 胡伟鹏, 李庆军, 曹珊珊. 空间刚性杆--弹簧组合结构轨道、姿态耦合动力学分析[J]. 力学学报, 2018, 50(1): 87-98. DOI: 10.6052/0459-1879-17-337
引用本文: 尹婷婷, 邓子辰, 胡伟鹏, 李庆军, 曹珊珊. 空间刚性杆--弹簧组合结构轨道、姿态耦合动力学分析[J]. 力学学报, 2018, 50(1): 87-98. DOI: 10.6052/0459-1879-17-337
Yin Tingting, Deng Zichen, Hu Weipeng, Li Qingjun, Cao Shanshan. DYNAMIC MODELLING AND SIMULATION OF ORBIT AND ATTITUDE COUPLING PROBLEMS FOR STRUCTURE COMBINED OF SPATIAL RIGID RODS AND SPRING[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(1): 87-98. DOI: 10.6052/0459-1879-17-337
Citation: Yin Tingting, Deng Zichen, Hu Weipeng, Li Qingjun, Cao Shanshan. DYNAMIC MODELLING AND SIMULATION OF ORBIT AND ATTITUDE COUPLING PROBLEMS FOR STRUCTURE COMBINED OF SPATIAL RIGID RODS AND SPRING[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(1): 87-98. DOI: 10.6052/0459-1879-17-337

空间刚性杆--弹簧组合结构轨道、姿态耦合动力学分析

基金项目: 国家自然科学基金资助项目 (11432010,11672241 和 11502202).
详细信息
    作者简介:

    *通讯作者:邓子辰,教授,主要研究方向:非线性动力学系统的保结构分析与控制. E-mail: dweifan@nwpu.edu.cn

    通讯作者:

    邓子辰

  • 中图分类号: O241,V476.5;

DYNAMIC MODELLING AND SIMULATION OF ORBIT AND ATTITUDE COUPLING PROBLEMS FOR STRUCTURE COMBINED OF SPATIAL RIGID RODS AND SPRING

  • 摘要: 以空间太阳帆塔在轨运行中遇到的强耦合动力学问题为研究背景,建立了空间刚性杆-- 弹簧组合结构轨道与姿态耦合 问题的动力学模型,采用辛 (几何) 算法研究了其轨道与姿态耦合的动力学行为,研究结果可以从系统的能量保持情况间接得到验 证. 首先,基于变分原理,通过引入对偶变量将描述空间刚性杆-- 弹簧组合结构动力学行为的拉格朗日方程导入哈 密尔顿体系,建立简化模型的正则控制方程;随后,采用辛龙格库塔方法模拟分析了地球非球摄动对轨道、姿态的影响及系统能 量的数值偏差问题. 数值模拟结果显示:随着初始姿态角速度增大,轨道半径的扰动 增大,轨道与姿态之间的耦合效应加剧; 带谐摄动对空间刚性杆-- 弹簧组合结构模型的轨道、姿态产生的影响比田谐摄动要高出至少两个数量级;同时辛龙格库塔方法能更好 地快速模拟地球非球摄动影响下空间刚性杆-- 弹簧组合结构的动力学行为,并能够长时间保持系统的总能量,有望为 超大空间结构实时反馈控制提供实时动力学响应结果.
    Abstract: For the strong coupling dynamic problems of the sail tower solar power satellite in orbit, a simplified model combined of spatial rigid rods and spring that describes the coupling dynamic behaviours of orbit and attitude is established. The coupling dynamic effects of the simplified model are analyzed by the symplectic geometry method and the numerical results can be verified indirectly by the energy conservation of the system. Firstly, based on the variational principle, by introducing the symplectic variables the Lagrange equation describing the dynamic behaviour of the simplified model combined by spatial rigid rods and spring is expressed in the form of the Hamilton system, and the associated canonical governing equations of the simplified model are established. And then, the influence of the Earth non-shape perturbation on the orbit, attitude coupling dynamic motion is simulated by the symplectic Runge-Kutta method and the energy deviation of the simplified model is also analyzed by the symplectic Runge-Kutta method. According to the numerical results, it can be concluded that with the increase of the initial attitude angle velocity, the disturbance of the orbital radius increases and the coupling dynamics between orbit and attitude increases. The effect of zonal harmonic term is higher than that of the tesseral harmonic term at least about two orders of magnitude. And the symplectic Runge-Kutta method proposed could reproduce the dynamic properties of the sail tower solar power satellite associated with the Earth non-shape perturbation rapidly and preserve the energy well with excellent long-time numerical stability, which will give a new approach to obtain the real-time dynamic response of the ultra-large spatial structure for the real-time feedback controller design.
  • [1] Fujii HA, Watanabe T, Kojima H, et al.Control of attitude and vibration of a tethered space solar power satellite//AIAA Guidance, Navigation and Control Conference and Exhibit, Austin, USA, August 11-14, 2003
    [2] Duboshin GN.On one particular case of the problem of the translational-rotational motion of two bodies.Soviet Astronomy, 1959, 3: 25
    [3] Jung WY, Mazzoleni AP, Chung JT.Dynamic analysis of a tethered satellite system with a moving mass.Nonlinear Dynamics, 2014, 75(1-2): 267-281
    [4] Lange B.Linear coupling between orbit and attitude motions of a rigid body.The Journal of the Astronautical Sciences, 1970, 18(3): 235
    [5] Wie B, Roithmayr CM.Attitude and orbit control of a very large geostationary solar power satellite.Journal of Guidance, Control, and Dynamics, 2005, 28(3): 439-451
    [6] Ishimura K, Higuchi K.Coupling among pitch motion, axial vibration, and orbital motion of large space structures.Journal of Aerospace Engineering, 2008, 21(2): 61-71
    [7] 邓子辰, 曹珊珊, 李庆军等. 基于辛Runge-Kutta方法的太阳帆塔动力学特性研究. 中国科学: 技术科学, 2016, 46: 1242-1253
    [7] Deng Zichen, Cao Shanshan, Li Qingjun, et al.Dynamic behavior of sail tower SPS based on the symplectic Runge-Kutta method. Science in China(Series E), 2016, 46: 1242-1253 (in Chinese)
    [8] 朱帅, 周钢, 刘晓梅等. 精细辛有限元方法及其相位误差研究. 力学学报, 2016, 48(2): 399-405
    [8] Zhu Shuai, Zhou Gang, Liu Xiaomei, et al.Precise symplectic time finite element method and the study of phase error.Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(2): 399-405 (in Chinese)
    [9] 郑丹丹, 罗建军, 张仁勇等. 基于混合Lie 算子辛算法的不变流形计算. 力学学报, 2017, 49(5): 1126-1134
    [9] Zheng Dandan, Luo Jianjun, Zhang Renyong, et al.Computation of invariant manifold based on symplectic algorithm of mixed Lie operator.Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(5): 1126-1134 (in Chinese)
    [10] 魏乙, 邓子辰, 李庆军等. 空间太阳能电站的轨道、姿态和结构振动的耦合动力学建模及辛求解. 动力学与控制学报, 2016, 14(6): 513-519
    [10] Wei Yi, Deng Zichen, Li Qingjun, et al.Coupling dynamic modeling among orbital motion, attitude motion and structural vibration and symplectic solution of SPS.Journal of Dynamics and Control, 2016, 14(6): 513-519 (in Chinese)
    [11] Hu WP, Song MZ, Deng ZC.Energy dissipation/transfer and stable attitude of spatial on-orbit tethered system.Journal of Sound and Vibration, 2018, 412: 58-73
    [12] 刘利生, 吴斌, 杨萍. 航天器精确定轨与自校准技术. 北京: 国防工业出版社, 2005: 98-100
    [12] Liu Lisheng, Wu Bin, Yang Ping.Orbit Precision Determination & Self-calibration Technique of Spacecraft. Beijing: Nation Defense Industry Press, 2005: 98-100 (in Chinese)
    [13] McNally I,Scheeres D,Radice G. Locating large solar power satellites in the geosynchronous Laplace plane.Journal of Guidance, Control, and Dynamics, 2015, 38(3): 489-505
    [14] Casanova D, Petit A, Lematre A.Long-term evolution of space debris under the J2 effect, the solar radiation pressure and the solar and lunar perturbations. Celestial Mechanics and Dynamical Astronomy, 2015, 123(2): 223-238
    [15] Liu JF, Cui NG, Shen F, et al.Dynamic modeling and analysis of a flexible sailcraft.Advances in Space Research, 2015 56(4): 693-713
    [16] 温生林, 闫野, 易腾. 超低轨道卫星摄动特性分析及轨道维持方法. 国防科技大学学报, 2015, 37(2): 128-134
    [16] Wen Shenglin, Yan Ye, Yi Teng.Analyzing perturbation characteristic and orbital maintenance strategy for super low altitude satellite.Journal of National University of Defense Technology, 2015, 37(2): 128-134 (in Chinese)
    [17] Feng K.On difference schemes and symplectic geometry//Proceeding of the 1984 Beijing Symposium on Differential Geometry and Differential Equations, Beijing: Science Press, 1984: 42-58
    [18] Hu WP, Li QJ, Jiang XH.Coupling dynamic behaviors of spatial flexible beam with weak damping.International Journal for Numerical Methods in Engineering, 2017, 111: 660-675
    [19] Seboldt W, Klimke M, Leipold M, et al.European Sail Tower SPS concept.Acta Astronaut, 2001, 48: 785-792
    [20] 文奋强, 邓子辰, 魏乙等. 太阳帆塔轨道和姿态耦合动力学建模及辛求解. 应用数学和力学, 2017, 38(7): 762-768
    [20] Wen Fenqiang, Deng Zichen, Wei Yi, et al.Dynamic modeling among coupled orbital-attitude motion and symplectic solution of solar sail tower.Applied Mathematics and Mechanics, 2017, 38(7): 762-768 (in Chinese)
    [21] 肖峰. 人造地球卫星轨道摄动理论. 长沙: 国防科技大学出版社, 1997: 50-54
    [21] Xiao Feng.Man-made Earth Satellite Orbit Perturbation Theory. Changsha: National University of Defense Technology Publishing House, 1997: 50-54 (in Chinese)
    [22] 李渊, 邓子辰, 叶学华等. 基于辛理论的载流碳纳米管能带分析. 力学学报, 2016, 48(1): 135-139
    [22] Li Yuan, Deng Zichen, Ye Xuehua, et al.Analysing the wave scattering in single-walled carbon nanotube conveying fluid based on the symplectic theory.Journal of Theoretical and Applied Mechanics, 2016, 48(1): 135-139 (in Chinese)
    [23] Feng K.Difference-schemes for Hamiltonian-formalism and symplectic-geometry.Journal of Computational mathematics, 1986, 4(3): 279-289
    [24] Sanz-Serna JM.Runge-Kutta schemes for Hamiltonian systems.BIT Numerical Mathematics, 1988, 28(4): 877-883
    [25] Sofroniou M, Oevel W.Symplectic Runge-Kutta schemes I: Order conditions.SIAM Journal on Numerical Analysis, 1997, 34(5): 2063-2086
    [26] Carrington C, Fikes J,Gerry M,et al.The abacus/reflector and integrated symmetrical concentrator: Concepts for space solar power collection and transmission//The 35th Intersociety Energy Conversion Engineering Conference and Exhibit, AIAA-2000-3067, Las Vegas, July, 2000
    [27] 章仁为. 卫星轨道姿态动力学与控制. 北京: 北京航空航天大学出版社, 1998: 50-53
    [27] Zhang Renwei.Orbit Attitude Dynamics and Control of Satellite. Beijing: Beijing University of Aeronautics and Astronautics Publishing House, 1998: 50-53 (in Chinese)
    [28] McNally I, Scheeres D, Radice G. Attitude dynamics of large geosynchronous solar power satellites//AIAA/AAS Astro dynamics Specialist Conference, AIAA, San Diego, CA, August, 2014
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    其他类型引用(10)

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出版历程
  • 收稿日期:  2017-11-09
  • 刊出日期:  2018-01-17

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