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刚-液耦合航天器系统的Hamilton结构及稳定性分析

易中贵 岳宝增 刘峰 卢涛 邓明乐

易中贵, 岳宝增, 刘峰, 卢涛, 邓明乐. 刚-液耦合航天器系统的Hamilton结构及稳定性分析[J]. 应用数学和力学, 2023, 44(5): 499-512. doi: 10.21656/1000-0887.430379
引用本文: 易中贵, 岳宝增, 刘峰, 卢涛, 邓明乐. 刚-液耦合航天器系统的Hamilton结构及稳定性分析[J]. 应用数学和力学, 2023, 44(5): 499-512. doi: 10.21656/1000-0887.430379
YI Zhonggui, YUE Baozeng, LIU Feng, LU Tao, DENG Mingle. Hamiltonian Structures and Stability Analysis for Rigid-Liquid Coupled Spacecraft Systems[J]. Applied Mathematics and Mechanics, 2023, 44(5): 499-512. doi: 10.21656/1000-0887.430379
Citation: YI Zhonggui, YUE Baozeng, LIU Feng, LU Tao, DENG Mingle. Hamiltonian Structures and Stability Analysis for Rigid-Liquid Coupled Spacecraft Systems[J]. Applied Mathematics and Mechanics, 2023, 44(5): 499-512. doi: 10.21656/1000-0887.430379

刚-液耦合航天器系统的Hamilton结构及稳定性分析

doi: 10.21656/1000-0887.430379
基金项目: 

国家国防科技工业局民用航天“十三五”技术预先研究项目 D020201

国家自然科学基金(重点项目) 12132002

国家自然科学基金(面上项目) 11772049

国家自然科学基金青年科学基金项目 12202044

详细信息
    作者简介:

    易中贵(1989—),男,博士(E-mail: yhcqyzg@sina.com)

    通讯作者:

    岳宝增(1962—),男,教授,博士(通讯作者. E-mail: bzyue@bit.edu.cn)

  • 中图分类号: O302

Hamiltonian Structures and Stability Analysis for Rigid-Liquid Coupled Spacecraft Systems

  • 摘要: 该文采用3D刚体摆来等效推进剂的非线性晃动行为. 由此研究了该刚-液耦合航天器系统的Hamilton结构,介绍了系统的$ \mathbb{R}^3$约化(对应系统的平移不变性或总线动量不变性)以及So(3)约化(对应系统的旋转不变性或总角动量不变性),并推导了系统在约化空间$ \mathfrak{s}_0^*(3) \times \mathfrak{s}_0^*(3) \times {S_0}(3)$上的约化Poisson括号. 接着研究了刚-液耦合航天器系统的自旋稳定性特征,先根据对称临界原理推导了刚-液耦合航天器系统的相对平衡态,由此根据能量-动量方法与分块对角化技术,推导了系统的自旋稳定性条件和Arnold形式的稳定性边界. 最后根据具体模型参数,给出了以图形方式展现的自旋稳定域.
  • 图  1  刚-液耦合航天器系统的等效力学模型

    Figure  1.  The equivalent mechanical model for the rigid-liquid coupled spacecraft system

    图  2  刚-液耦合航天器系统的稳定域

    Figure  2.  Stability regions of the rigid-liquid coupled spacecraft system

  • [1] DODGE F T. The new "dynamic behavior of liquids in moving containers"[R]. San Antonio, TX, USA: Southwest Research Institute, 2000.
    [2] IBRAHIM R A. Liquid Sloshing Dynamics: Theory and Applications[M]. Cambridge: Cambridge University Press, 2005.
    [3] KANA D D. Validated spherical pendulum model for rotary liquid slosh[J]. Journal of Spacecraft and Rockets, 1989, 26(3): 188-195. doi: 10.2514/3.26052
    [4] KANG J Y, LEE S. Attitude acquisition of a satellite with a partially filled liquid tank[J]. Journal of Guidance, Control, and Dynamics, 2008, 31(3): 790-793. doi: 10.2514/1.31865
    [5] MIAO N, LI J F, WANG T S. Equivalent mechanical model of large-amplitude liquid sloshing under time-dependent lateral excitations in low-gravity conditions[J]. Journal of Sound and Vibration, 2017, 386: 421-432. doi: 10.1016/j.jsv.2016.08.029
    [6] YUE B Z. Study on the chaotic dynamics in attitude maneuver of liquid-filled flexible spacecraft[J]. AIAA Journal, 2011, 49(10): 2090-2099. doi: 10.2514/1.J050144
    [7] 邓明乐. 液体大幅晃动等效力学模型及航天器刚-液-柔-控耦合动力学研究[D]. 博士学位论文. 北京: 北京理工大学, 2017.

    DENG Mingle. Studies on the equivalent mechanical model of large amplitude liquid slosh and rigid-liquid-flex-control coupling dynamics of spacecraft[D]. PhD Thesis. Beijing: Beijing Institute of Technology, 2017. (in Chinese)
    [8] TANG Y, YUE B Z. Simulation of large-amplitude three-dimensional liquid sloshing in spherical tanks[J]. AIAA Journal, 2017, 55(6): 2052-2059. doi: 10.2514/1.J055798
    [9] 刘峰. 液体非线性晃动类柔性航天器大范围运动动力学与姿态控制研究[D]. 博士学位论文. 北京: 北京理工大学, 2020.

    LIU Feng. Studies on large motion dynamics and attitude control of flexible spacecraft with nonlinear liquid slosh[D]. PhD Thesis. Beijing: Beijing Institute of Technology, 2020. (in Chinese)
    [10] LIU F, YUE B Z, TANG Y, et al. 3DOF-rigid-pendulum analogy for nonlinear liquid slosh in spherical propellant tanks[J]. Journal of Sound and Vibration, 2019, 460: 114907. doi: 10.1016/j.jsv.2019.114907
    [11] ABRAHAM R, MARSDEN J E. Foundations of Mechanics[M]. New York: Addison-Wesley, 1978.
    [12] MARSDEN J E, RATIU T S. Introduction to Mechanics and Symmetry: a Basic Exposition of Classical Mechanical Systems[M]. New York: Springer, 1998.
    [13] HOLM D D, MARSDEN J E, RATIU T, et al. Nonlinear stability of fluid and plasma equilibria[J]. Physics Reports, 1985, 123(1/2): 1-116. http://www.sciencedirect.com/science/article/pii/0370157385900286
    [14] KRISHNAPRASAD P S, MARSDEN J E. Hamiltonian structures and stability for rigid bodies with flexible attachments[J]. Archive for Rational Mechanics and Analysis, 1987, 98(1): 71-93. doi: 10.1007/BF00279963
    [15] OZKAZANC Y. Dynamics and stability of spacecraft with fluid-filled containers[D]. PhD Thesis. MD, USA: University of Maryland, 1994.
    [16] ARDAKANI H A, BRIDGES T J, GAY-BALMAZ F, et al. A variational principle for fluid sloshing with vorticity, dynamically coupled to vessel motion[J]. Proceedings of the Royal Society A, 2019, 475(2224): 20180642. doi: 10.1098/rspa.2018.0642
    [17] GASBARRI P, SABATINI M, PISCULLI A. Dynamic modelling and stability parametric analysis of a flexible spacecraft with fuel slosh[J]. Acta Astronautica, 2016, 127: 141-159. doi: 10.1016/j.actaastro.2016.05.018
    [18] SALMAN A, YUE B Z. Bifurcation and stability analysis of the Hamiltonian-Casimir model of liquid sloshing[J]. Chinese Physics Letters, 2012, 29(6): 060501. doi: 10.1088/0256-307X/29/6/060501
    [19] 闫玉龙. 航天器刚液柔耦合动力学及姿态稳定性研究[D]. 博士学位论文. 北京: 北京理工大学, 2017.

    YAN Yulong. Study on dynamics and attitude stability of the rigid-liquid-flex coupling spacecraft system[D]. PhD Thesis. Beijing: Beijing Institute of Technology, 2017. (in Chinese)
    [20] SIMO J C, POSBERGH T A, MARSDEN J E. Stability of coupled rigid body and geometrically exact rods: block diagonalization and the energy-momentum method[J]. Physics Reports, 1990, 193(6): 279-360. doi: 10.1016/0370-1573(90)90125-L
    [21] SIMO J C, LEWIS D, MARSDEN J E. Stability of relative equilibria, part Ⅰ: the reduced energy-momentum method[J]. Archive for Rational Mechanics and Analysis, 1991, 115(1): 15-59. doi: 10.1007/BF01881678
    [22] SIMO J C, POSBERGH T A, MARSDEN J E. Stability of relative equilibria, part Ⅱ: application to nonlinear elasticity[J]. Archive for Rational Mechanics and Analysis, 1991, 115(1): 61-100. doi: 10.1007/BF01881679
    [23] YI Z G, YUE B Z. Study on the dynamics, relative equilibria, and stability for liquid-filled spacecraft with flexible appendage[J]. Acta Mechanica, 2022, 233(9): 3557-3578. doi: 10.1007/s00707-022-03269-5
    [24] ABRAMSON H N. The dynamic behavior of liquids in moving containers, with applications to space vehicle technology: NASA-SP-106[R]. San Antonio, TX, USA: Southwest Research Institute, 1966.
    [25] GROSSMAN R, KRISHNAPRASAD P S, MARSDEN J E. The dynamics of two coupled rigid bodies[J]. Dynamical Systems Approaches to Nonlinear Problems in Systems and Circuits, 1987, 1988: 373-378. http://drum.lib.umd.edu/bitstream/handle/1903/4531/TR_87-22.pdf?sequence=1&isAllowed=y
    [26] KRISHNAPRASAD P. Lie-Poisson structures, dual-spin spacecraft and asymptotic stability[J]. Nonlinear Analysis: Theory, Methods & Applications, 1985, 9(10): 1011-1035. http://www.sciencedirect.com/science/article/pii/0362546X85900835/part/first-page-pdf
    [27] OH Y G, SREENATH N, KRISHNAPRASAD P, et al. The dynamics of coupled planar rigid bodies Ⅱ: bifurcations, periodic solutions, and chaos[J]. Journal of Dynamics and Differential Equations, 1989, 1(3): 269-298. doi: 10.1007/BF01053929
    [28] SREENATH N, OH Y G, KRISHNAPRASAD P, et al. The dynamics of coupled planar rigid bodies, part Ⅰ: reduction, equilibria and stability[J]. Dynamics and Stability of Systems, 1988, 3(1/2): 25-49. http://doc.paperpass.com/foreign/rgArti1988139257856.html
    [29] WANG LISHENG, KRISHNAPRASAD P S. Gyroscopic control and stabilization[J]. Journal of Nonlinear Science, 1992, 2(4): 367-415. doi: 10.1007/BF01209527
    [30] GE X S, YI Z G, CHEN L Q. Optimal control of attitude for coupled-rigid-body spacecraft via Chebyshev-Gauss pseudospectral method[J]. Applied Mathematics and Mechanics, 2017, 38(9): 1257-1272. doi: 10.1007/s10483-017-2236-8
    [31] MARSDEN J E, WEINSTEIN A. Reduction of symplectic manifolds with symmetry[J]. Reports on Mathematical Physics, 1974, 5(1): 121-130. doi: 10.1016/0034-4877(74)90021-4
    [32] MARSDEN J E, RATIU T. Reduction of Poisson manifolds[J]. Letters in Mathematical Physics, 1986, 11(2): 161-169. doi: 10.1007/BF00398428
    [33] 易中贵. 几何力学建模和谱方法离散及航天工程应用[D]. 博士学位论文. 北京: 北京理工大学, 2022.

    YI Zhonggui. Geometric mechanics modeling and spectral methods discretization and aerospace engineering applications[D]. PhD Thesis. Beijing: Beijing Institute of Technology, 2022. (in Chinese)
    [34] SHI D H, ZENKOV D V, BLOCH A M. Hamel's formalism for classical field theories[J]. Journal of Nonlinear Science, 2020, 30(1): 1307-1353. http://d.wanfangdata.com.cn/periodical/9b0df1df64c9df5bcf813e0802b2e532
    [35] SIMO J C, MARSDEN J E, KRISHNAPRASAD P. The Hamiltonian structure of nonlinear elasticity: the material and convective representations of solids, rods, and plates[J]. Archive for Rational Mechanics and Analysis, 1988, 104(2): 125-183. doi: 10.1007/BF00251673
    [36] POSBERGH T A, KRISHNAPRASAD P S, MARSDEN J E. Stability analysis of a rigid body with a flexible attachment using the energy-Casimir method: SRC-TR-87-23[R]. MD, USA: University of Maryland, 1987.
    [37] YI Z G, YUE B Z, DENG M. Hamilton-Pontryagin spectral-collocation methods for the orbit propagation[J]. Acta Mechanica Sinica, 2021, 37(11): 1698-1715. http://www.sciengine.com/doi/pdf/88730759c9fe4886b0a3881299112762
    [38] 冯康, 秦孟兆. 哈密尔顿系统的辛几何算法[M]. 杭州: 浙江科学技术出版社, 2003.

    FENG Kang, QIN Mengzhao. Symplectic Geometric Algorithms for Hamiltonian Systems[M]. Hangzhou: Zhejiang Science and Technology Press, 2003. (in Chinese)
    [39] 高山, 史东华, 郭永新. Hamel框架下几何精确梁的离散动量守恒律[J]. 力学学报, 2021, 53(6): 1712-1719. https://www.cnki.com.cn/Article/CJFDTOTAL-LXXB202106017.htm

    GAO Shan, SHI Donghua, GUO Yongxin. Discrete momentum conservation law of geometrically exact beam in Hamel's framework[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(6): 1712-1719. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-LXXB202106017.htm
    [40] 满淑敏, 高强, 钟万勰. 非完整约束Hamilton动力系统保结构算法[J]. 应用数学和力学, 2020, 41(6): 581-590. doi: 10.21656/1000-0887.400375

    MAN Shumin, GAO Qiang, ZHONG Wanxie. A structure-preserving algorithm for Hamiltonian systems with nonholonomic constraints[J]. Applied Mathematics and Mechanics, 2020, 41(6): 581-590. (in Chinese) doi: 10.21656/1000-0887.400375
    [41] 刘晓梅, 周钢, 朱帅. Hamilton系统下基于相位误差的精细辛算法[J]. 应用数学和力学, 2019, 40(6): 595-608. doi: 10.21656/1000-0887.390249

    LIU Xiaomei, ZHOU Gang, ZHU Shuai. A highly precise symplectic direct integration method based on phase errors for Hamiltonian systems[J]. Applied Mathematics and Mechanics, 2019, 40(6): 595-608. (in Chinese) doi: 10.21656/1000-0887.390249
    [42] 张素英, 邓子辰. Poisson流形上广义Hamilton系统的保结构算法[J]. 西北工业大学学报, 2002, 20(4): 625-628. https://www.cnki.com.cn/Article/CJFDTOTAL-XBGD200204030.htm

    ZHANG Suying, DENG Zichen. An algorithm for preserving the generalized Poisson bracket structure of generalized Hamiltonian system[J]. Journal of Northwestern Polytechnical University, 2002, 20(4): 625-628. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-XBGD200204030.htm
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  • 收稿日期:  2022-06-13
  • 修回日期:  2022-08-12
  • 刊出日期:  2023-05-01

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