Astrophysics and Space Science

, Volume 355, Issue 2, pp 203–212 | Cite as

Attitude stability of a dual-spin spacecraft on a stationary orbit around an asteroid subjected to gravity gradient torque

Original Article

Abstract

The attitude stability of a dual-spin spacecraft on a stable stationary orbit around an asteroid subjected to gravity gradient torque is studied in this paper, in which the effect of the second order and degree harmonics C20 and C22 of the gravity field of the asteroid is involved. Under some reasonable assumptions, the linearized equations of attitude motion of the dual-spin spacecraft with a nutation damper are presented. Then the necessary and sufficient conditions of attitude stability of the dual-spin spacecraft with a nutation damper are derived. Meantime, the linearized equations of attitude motion and the conditions of attitude stability of the dual-spin spacecraft without a nutation damper are also presented. These results are generalized and encompass a series of special cases, and from which some useful conclusions on the attitude stability of the dual-spin spacecraft are obtained. Examples are given to illustrate the application of these conditions of attitude stability.

Keywords

Attitude stability Dual-spin spacecraft Asteroid Conditions of stability 

Notes

Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant nos. 11125315, 11033009 and 11103086. The authors would like to thank anonymous reviewer for the valuable comments that help to substantially improve the manuscript.

References

  1. Aslanov, V.S., Yudintsev, V.V.: Dynamics and control of dual-spin gyrostat spacecraft with changing structure. Celest. Mech. Dyn. Astron. 115(1), 91–105 (2013)ADSMathSciNetCrossRefMATHGoogle Scholar
  2. Bainum, P.M., Fuechsel, P.G., Mackison, D.L.: Motion and stability of a dual-spin satellite with nutation damping. J. Spacecr. Rockets 7(6), 690–696 (1970)ADSCrossRefGoogle Scholar
  3. Curtis, H.D.: Orbital Mechanics for Engineering Students. Elsevier/Butterworth-Heinemann, Amsterdam/Stoneham (2005)Google Scholar
  4. Fujiwara, A., Kawaguchi, J., Yeomans, D.K., Abe, M., Mukai, T., Okada, T., Saito, J., Yano, H., Yoshikawa, M., Scheeres, D.J., Barnouin-Jha, O., Cheng, A.F., Demura, H., Gaskell, R.W., Hirata, N., Ikeda, H., Kominato, T., Miyamoto, H., Nakamura, A.M., Nakamura, R., Sasaki, S., Uesugi, K.: The rubble-pile asteroid Itokawa as observed by Hayabusa. Science 312(5778), 1330–1334 (2006)ADSCrossRefGoogle Scholar
  5. Ge, X.S.: The stability of dual spinner with elastic axis in gravitational field. Shanghai J. Mech. 18(4), 327–331 (1997)Google Scholar
  6. Hall, C.D., Rand, R.H.: Spinup dynamics of axial dual-spin spacecraft. J. Guid. Control Dyn. 17(1), 30–37 (1994)ADSCrossRefGoogle Scholar
  7. Han, G.C., Zhang, Y.L.: Dynamic attitude equations and stability study of dual spinning satellites. J. Harbin Eng. Univ. 25(1), 94–99 (2004)Google Scholar
  8. Hu, W.: Orbital motion in uniformly rotating second degree and order gravity fields. Ph.D. Dissertation, Department of Aerospace Engineering, The University of Michigan, Michigan (2002)Google Scholar
  9. Huang, J., Ji, J., Ye, P., Wang, X., Yan, J., Meng, L., Wang, S., Li, C., Li, Y., Qiao, D., Zhao, W., Zhao, Y., Zhang, T., Liu, P., Jiang, Y., Rao, W., Li, S., Huang, C., Ip, W., Hu, S., Zhu, M., Yu, L., Zou, Y., Tang, X., Li, J., Zhao, H., Huang, H., Jiang, X., Bai, J.: The ginger-shaped asteroid 4179 Toutatis: new observations from a successful flyby of Chang’e-2. Sci. Rep. 3, 3411 (2013)ADSCrossRefGoogle Scholar
  10. Jin, L.: Liapunov stability criteria for dual spin satellites with flexible appendages. J. Natl. Univ. Defense Technol. 13(3), 1–9 (1991)ADSGoogle Scholar
  11. Kumar, K.D.: Attitude dynamics and control of satellites orbiting rotating asteroids. Acta Mech. 198(1–2), 99–118 (2008)CrossRefMATHGoogle Scholar
  12. Liang, C., Li, Y.: Attitude analysis and robust adaptive backstepping sliding mode control of spacecrafts orbiting irregular asteroids. Math. Probl. Eng. 2014, 367163 (2014). (15 pp.)MathSciNetGoogle Scholar
  13. Likins, P.W.: Attitude stability criteria for dual spin spacecraft. J. Spacecr. Rockets 4(12), 1638–1643 (1967)ADSCrossRefGoogle Scholar
  14. Misra, A.K., Panchenko, Y.: Attitude dynamics of satellites orbiting an asteroid. J. Astronaut. Sci. 54(3&4), 369–381 (2006)ADSMathSciNetCrossRefGoogle Scholar
  15. Meng, Y., Hao, R., Chen, Q.: Attitude stability analysis of a dual-spin spacecraft in halo orbits. Acta Astron. 99, 318–329 (2014)CrossRefGoogle Scholar
  16. Or, A.C.: Chaotic motions of a dual-spin body. J. Appl. Mech. 65(1), 150–156 (1998)ADSCrossRefGoogle Scholar
  17. Papusha, A.N.: Free motion of a system of rigid bodies with dual-spin rotation. Int. Appl. Mech. 21(8), 816–822 (1985)ADSMathSciNetMATHGoogle Scholar
  18. Papusha, A.N.: Free motion of a system of rigid bodies with dual spin, provided with nutation dampers. Int. Appl. Mech. 22(10), 995–1000 (1986)ADSMATHGoogle Scholar
  19. Riverin, J.L., Misra, A.K.: Attitude dynamics of satellites orbiting small bodies. AIAA/AAS Astrodyn. Spec. Conf. Exhib., AIAA 4520, 5–8 (2002)Google Scholar
  20. Scheeres, D.J., Ostro, S.J., Hudson, R.S., Werner, R.A.: Orbits close to asteroid 4769 Castalia. Icarus 121(1), 67–87 (1996)ADSCrossRefGoogle Scholar
  21. Tsuchiya, K.: Attitude behavior of a dual-spin spacecraft composed of asymmetric bodies. J. Guid. Control Dyn. 2(4), 328–333 (1979)ADSCrossRefMATHGoogle Scholar
  22. Veverka, J., Thomas, P., Harch, A., Clark, B., Bell, J.F., Carcich, B., Joseph, J., Chapman, C., Merline, W., Robinson, M., Malin, M., McFadden, L.A., Murchie, S., Hawkins, S.E., Farquhar, R., Izenberg, N., Cheng, A.: NEAR’s flyby of 253 Mathilde: images of a C asteroid. Science 278(5346), 2109–2114 (1997)ADSCrossRefGoogle Scholar
  23. Wang, Y., Xu, S.: Analysis of gravity-gradient-perturbed attitude dynamics on a stationary orbit around an asteroid via dynamical systems theory. AIAA/AAS Astrodyn. Spec. Conf., AIAA 5059, 13–16 (2012)Google Scholar
  24. Wang, Y., Xu, S.: Equilibrium attitude and stability of a spacecraft on a stationary orbit around an asteroid. Acta Astron. 84, 99–108 (2013a)CrossRefGoogle Scholar
  25. Wang, Y., Xu, S.: Attitude stability of a spacecraft on a stationary orbit around an asteroid subjected to gravity gradient torque. Celest. Mech. Dyn. Astron. 115(4), 333–352 (2013b)ADSMathSciNetCrossRefGoogle Scholar
  26. Wang, Y., Xu, S.: Equilibrium attitude and nonlinear attitude stability of a spacecraft on a stationary orbit around an asteroid. Adv. Space Res. 52(8), 1497–1510 (2013c)ADSCrossRefGoogle Scholar
  27. Wang, Y., Xu, S.: Gravity gradient torque of spacecraft orbiting asteroids. Aircr. Eng. Aerosp. Technol. 85(1), 72–81 (2013d)MathSciNetCrossRefGoogle Scholar
  28. Wang, Y., Xu, S.: Analysis of the attitude dynamics of a spacecraft on a stationary orbit around an asteroid via Poincaré section. Aerosp. Sci. Technol. (2014). doi: 10.1016/j.ast.2014.06.010
  29. Xu, W.B., Zhao, H.B.: Deep space exploration of asteroids: the science perspectives. Adv. Earth Sci. 20(11), 1183–1190 (2005)MathSciNetGoogle Scholar
  30. Zhang, M.J., Zhao, C.Y.: Attitude stability of a spacecraft with two flexible solar arrays on a stationary orbit around an asteroid subjected to gravity gradient torque. Astrophys. Space Sci. 351(2), 507–524 (2014)ADSCrossRefGoogle Scholar
  31. Zuber, M.T., Smith, D.E., Cheng, A.F., Garvin, J.B., Aharonson, O., Cole, T.D., Dunn, P.J., Guo, Y., Lemoine, F.G., Neumann, G.A., Rowlands, D.D., Torrence, M.H.: The shape of 433 Eros from the NEAR-Shoemaker laser rangefinder. Science 289(5487), 2097–2101 (2000)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Purple Mountain ObservatoryChinese Academy of SciencesNanjingChina
  2. 2.Key Laboratory of Space Object and Debris ObservationPMO, CASNanjingChina
  3. 3.University of Chinese Academy of SciencesBeijingChina

Personalised recommendations