Nonlinear Dynamics

, Volume 75, Issue 1–2, pp 267–281 | Cite as

Dynamic analysis of a tethered satellite system with a moving mass

Original Paper

Abstract

This paper presents a dynamic analysis of a tethered satellite system with a moving mass. A dynamic model with four degrees of freedom, i.e., a two-piece dumbbell model, is established for tethered satellites conveying a mass between them along the tether length. This model includes two satellites and a moving mass, treated as particles in a single orbital plane, which are connected by massless, straight tethers. The equations of motion are derived by using Lagrange’s equations. From the equations of motion, the dynamic response of the system when the moving mass travels along the tether connecting the two satellites is computed and analyzed. We investigate the global tendencies of the libration angle difference (between the two sections of tether) with respect to the changes in the system parameters, such as the initial libration angle, size (i.e. mass) of the moving mass, velocity of the moving mass, and tether length. We also present an elliptic orbit case and show that the libration angles and their difference increase as orbital eccentricity increases. Finally, our results show that a one-piece dumbbell model is qualitatively valid for studying the system under certain conditions, such as when the initial libration angles, moving mass velocity, and moving mass size are small, the tether length is large, and the mass ratio of the two satellites is large.

Keywords

Nonlinear dynamics Tethered satellites Dumbbell model Moving mass Libration angle 

References

  1. 1.
    Kirchgraber, U., Manz, U., Stoffer, D.: Rigorous proof of chaotic behaviour in a dumbbell satellite model. J. Math. Anal. Appl. 251(2), 897–911 (2000) CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Cho, S., Lovell, T.A., Cochran, J.E., Cicci, D.A.: Approximate solutions for tethered satellite motion. J. Guid. Control Dyn. 24(4), 746–754 (2001) CrossRefGoogle Scholar
  3. 3.
    Nakanishi, K., Kojima, H., Watanabe, T.: Trajectories of in-plane periodic solutions of tethered satellite system projected on van der Pol planes. Acta Astronaut. 68(7–8), 1024–1030 (2011) CrossRefGoogle Scholar
  4. 4.
    Mantri, P., Mazzoleni, A.P., Padgett, D.A.: Parametric study of deployment of tethered satellite systems. J. Spacecr. Rockets 44(2), 412–424 (2007) CrossRefGoogle Scholar
  5. 5.
    Williams, P.: Libration control of tethered satellites in elliptical orbits. J. Spacecr. Rockets 43(2), 476–479 (2006) CrossRefGoogle Scholar
  6. 6.
    Wen, H., Jin, D.P., Hu, H.Y.: Advances in dynamics and control of tethered satellite systems. Acta Mech. Sin. 24(3), 229–241 (2008) CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    Steindl, A., Troger, H.: Optimal control of deployment of a tethered subsatellite. Nonlinear Dyn. 31(3), 257–274 (2003) CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Wen, H., Jin, D.P., Hu, H.Y.: Optimal feedback control of the deployment of a tethered subsatellite subject to perturbations. Nonlinear Dyn. 51(4), 501–514 (2008) CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    Jin, D.P., Hu, H.Y.: Optimal control of a tethered subsatellite of three degrees of freedom. Nonlinear Dyn. 46(1–2), 161–178 (2006) CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    Williams, P.: Deployment/retrieval optimization for flexible tethered satellite systems. Nonlinear Dyn. 52(1–2), 159–179 (2008) CrossRefMATHGoogle Scholar
  11. 11.
    Cohen, S.S., Misra, A.K.: The effect of climber transit on the space elevator dynamics. Acta Astronaut. 64(5–6), 538–553 (2009) CrossRefGoogle Scholar
  12. 12.
    Woo, P., Misra, A.K.: Dynamics of a partial space elevator with multiple climbers. Acta Astronaut. 67(7–8), 753–763 (2010) CrossRefGoogle Scholar
  13. 13.
    Williams, P., Ockels, W.: Climber motion optimization for the tethered space elevator. Acta Astronaut. 66(9–10), 1458–1467 (2010) CrossRefGoogle Scholar
  14. 14.
    Steindl, A., Troger, H.: Is the sky-hook configuration stable? Nonlinear Dyn. 40(4), 419–431 (2005) CrossRefMATHMathSciNetGoogle Scholar
  15. 15.
    Fujii, H.A., Watanabe, T., Kusagaya, T., Sato, D., Ohta, M.: Dynamics of a flexible space tether equipped with a crawler mass. J. Guid. Control Dyn. 31(2), 436–440 (2008) CrossRefGoogle Scholar
  16. 16.
    Kojima, H., Sugimoto, Y., Furukawa, Y.: Experimental study on dynamics and control of tethered satellite systems with climber. Acta Astronaut. 69(1–2), 96–108 (2011) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Wonyoung Jung
    • 1
  • Andre P. Mazzoleni
    • 2
  • Jintai Chung
    • 1
  1. 1.Department of Mechanical EngineeringHanyang UniversityAnsanRepublic of Korea
  2. 2.Department of Mechanical and Aerospace EngineeringNorth Carolina State UniversityRaleighUSA

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