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Acta Mechanica Sinica

, Volume 32, Issue 1, pp 144–155 | Cite as

Coupling dynamic analysis of spacecraft with multiple cylindrical tanks and flexible appendages

  • Wen-Jun Wu
  • Bao-Zeng YueEmail author
  • Hua Huang
Research Paper

Abstract

This paper is mainly concerned with the coupling dynamic analysis of a complex spacecraft consisting of one main rigid platform, multiple liquid-filled cylindrical tanks, and a number of flexible appendages. Firstly, the carrier potential function equations of liquid in the tanks are deduced according to the wall boundary conditions. Through employing the Fourier–Bessel series expansion method, the dynamic boundaries conditions on a curved free-surface under a low-gravity environment are transformed to general simple differential equations and the rigid-liquid coupled sloshing dynamic state equations of liquid in tanks are obtained. The state vectors of rigid-liquid coupled equations are composed with the modal coordinates of the relative potential function and the modal coordinates of wave height. Based on the Bernoulli–Euler beam theory and the D’Alembert’s principle, the rigid-flexible coupled dynamic state equations of flexible appendages are directly derived, and the coordinate transform matrixes of maneuvering flexible appendages are precisely computed as time-varying. Then, the coupling dynamics state equations of the overall system of the spacecraft are modularly built by means of the Lagrange’s equations in terms of quasi-coordinates. Lastly, the coupling dynamic performances of a typical complex spacecraft are studied. The availability and reliability of the presented method are also confirmed.

Graphic abstract

Keywords

Multiple liquid-filled cylindrical tanks The Fourier–Bessel series expansion method Low-gravity environment  Maneuvering flexible appendages The Lagrange’s equations in terms of quasi-coordinates 

Notes

Acknowledgments

The project was supported by the National Natural Science Foundation of China (Grants 11472041, 11302244, 11532002) and Guangxi Natural Science Foundation (2015GXNSFBA139013).

References

  1. 1.
    Peterson, L.D., Crawley, E.F., Hansman, R.J.: Nonlinear fluid slosh coupled to the dynamics of a spacecraft. AIAA J. 27, 1230–1240 (1989). doi: 10.2514/3.10250 CrossRefGoogle Scholar
  2. 2.
    Huang, R.J., Long, Y.T., Chi, Y.M.: Sloshing dynamics coupled with spacecraft attitude dynamics part I: Formulation and theory. J. Spacecr. Rockets 33, 575–581 (1996). doi: 10.2514/3.26802 CrossRefzbMATHGoogle Scholar
  3. 3.
    Huang, R.J., Long, Y.T., Chi, Y.M.: Sloshing dynamics coupled with spacecraft attitude dynamics part II: Orbital environment application. J. Spacecr. Rockets 33, 582–593 (1996). doi: 10.2514/3.26803 CrossRefGoogle Scholar
  4. 4.
    Yue, B.Z.: Nonlinear coupled dynamics of liquid-filled spherical container in microgravity. Appl. Math. Mech. 29, 1085–1092 (2008). doi: 10.1007/s10483-008-0812-y CrossRefGoogle Scholar
  5. 5.
    Yue, B.Z.: Chaotic attitude and reorientation maneuver for completely liquid-filled spacecraft with flexible appendage. Acta Mech. Sin. 25, 271–277 (2009). doi: 10.1007/s10409-008-0213-7 CrossRefzbMATHGoogle Scholar
  6. 6.
    Yue, B.Z., Yang, D.D.: Study on the global chaotic dynamics and control of liquid-filled spacecraft with flexible appendage. Acta Mech. 209, 11–25 (2010). doi: 10.1007/s00707-009-0150-y CrossRefzbMATHGoogle Scholar
  7. 7.
    Yue, B.Z., Song, X.J.: Heteroclinic bifurcations in attitude maneuver of coupled slosh-spacecraft with flexible appendage. Sci. China Technol. Sci. 54, 2090–2099 (2011). doi: 10.1007/s11431-011-4476-z CrossRefzbMATHGoogle Scholar
  8. 8.
    Yang, D.D., Yue, B.Z., Wu, W.J., et al.: Attitude maneuver of liquid-filled spacecraft with a flexible appendage by momentum wheel. Acta Mech. Sin. 28, 542–550 (2012). doi: 10.1007/s10409-012-0060-4
  9. 9.
    Yue, B.Z.: Study on the chaotic dynamics in attitude maneuver of liquid-filled flexible spacecraft. AIAA J. 49, 2090–2099 (2012). doi: 10.2514/1.J050144 CrossRefGoogle Scholar
  10. 10.
    Ibrahim, R.A.: Liquid Sloshing Dynamics: Theory and Applications. Cambridge University Press, Cambridge (2005)CrossRefGoogle Scholar
  11. 11.
    Dodge, F.T., Garza, L.R.: Experimental and theoretical studies of liquid sloshing at simulated low gravity. J. Appl. Mech. 34, 555–562 (1967). doi: 10.1115/1.3607743 CrossRefGoogle Scholar
  12. 12.
    Wu, W.J., Yue, B.Z.: An analytical method for studying the sloshing properties of liquid in cylindrical tank under low gravity environment. J. Astron. 35, 397–406 (2014)Google Scholar
  13. 13.
    Wu, W.J., Yue, B.Z.: Low-gravity liquid sloshing in cylindrical tanks under pitching excitation. Chin. J. Theo. Appl. Mech. 46, 284–290 (2014)Google Scholar
  14. 14.
    Meirovitch, L., Quinn, R.D.: Equations of motion for maneuvering flexible spacecraft. J. Guid. Control Dyn. 10, 453–465 (1987). doi: 10.2514/3.20240 CrossRefzbMATHGoogle Scholar
  15. 15.
    Meirovitch, L., Kwak, M.K.: State equation for a spacecraft with maneuvering flexible appendages in terms of quasi-coordinates. Appl. Mech. Rev. 42, 161–170 (1989). doi: 10.1115/1.3152387 CrossRefMathSciNetGoogle Scholar
  16. 16.
    Kane, T.R., Ryan, R.R., Banerjee, A.K.: Dynamics of a cantilever beam attached to a moving base. J. Guid. Control Dyn. 10, 139–151 (1987). doi: 10.2514/3.20195 CrossRefGoogle Scholar
  17. 17.
    Meirovitch, L.: Methods of Analytical Dynamics. Dover Publications, New York (1970)Google Scholar
  18. 18.
    Meirovitch, L., Kwak, M.K.: Dynamics and control of spacecraft with retargeting flexible antennas. J. Guid. Control Dyn. 13, 241–248 (1990). doi: 10.2514/3.20543 CrossRefMathSciNetGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.School of Aerospace EngineeringBeijing Institute of TechnologyBeijingChina
  2. 2.School of Automobile and Traffic EngineeringGuangxi University of Science and TechnologyLiuzhouChina
  3. 3.Satellite Communication DepartmentChina Academy of Space TechnologyBeijingChina

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