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Application of Chebyshev collocation method for relocating of spacecrafts in Hill’s frame

  • Jai KumarEmail author
Article
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Abstract

In this study, the Chebyshev collocation method is used for solving the spacecraft relative motion of equations in Hill’s frame. Three different models of governing equations of relative motion (M1, M2, and M3) are considered and the maneuver cost required moving the spacecraft from one state to another is computed in the form of delta velocity at the first terminal point as a function of time of flight (TOF) and inter-satellite distance (ISD). A quantitative as well as qualitative difference is observed in the maneuver cost with the inclusion of radial and/or out of plane separation in along track separation of chaser. Also, a relative comparison of path profiles is made by considering M1, M2 and M3 models. Path profiles for M3 model are found close to M2 model for short intervals for a fixed ISD, whereas path profiles for M2 and M3 do not match even for small values of ISD for a fixed but long TOF. Path profiles for M1 models match to M2 model for very low values of target orbit eccentricities.

Keywords

Docking TPBVP Chebyshev collocation method CW equations relative motion 

References

  1. Bhowmik, M., Bera, P., Kumar, J. 2015, Int. J. Heat Fluid Flow 56, 272–283CrossRefGoogle Scholar
  2. Boyd, J.P. 2000, Chebyshev and Fourier Spectral Methods, 2nd edition, Dover, Inc., New YorkGoogle Scholar
  3. Campbell, M.E. 2003, J. Guidance, Control, Dynamics 26(5), 770–780ADSCrossRefGoogle Scholar
  4. Carter, T.E. 1990, J. Guidance, Control, Dynamics 13(1), 183–186ADSMathSciNetCrossRefGoogle Scholar
  5. Carter, T.E. 1998, J. Guidance, Control, Dynamics 21(1), 148–155ADSMathSciNetCrossRefGoogle Scholar
  6. Chen, Q., Dai, J. 2011, J. Guidance, Control, Dynamics 34(1), 287–293ADSCrossRefGoogle Scholar
  7. Cheng, X., Li, H., Zhang, R. 2017a, Nonlinear Dynamics 89(4), 2795–2814MathSciNetCrossRefGoogle Scholar
  8. Cheng, X., Li, H., Zhang, R. 2017b, Aerospace Sci. Technol. 66, 140–151CrossRefGoogle Scholar
  9. Clohessy, W.H., Wiltshire, R.S. 1960, J. Aerospace Sci. 27(9), 653–658CrossRefGoogle Scholar
  10. Guibout, V.M., Scheeres, D.J. 2004, J. Guidance, Control, Dynamics 27(4), 693–704ADSCrossRefGoogle Scholar
  11. Hill, G.W. 1878, Am. J. Math. 1, 5–26CrossRefGoogle Scholar
  12. Ichimura, Y., Ichikawa, A. 2008, J. Guidance, Control, Dynamics 31(4), 1014–1027ADSCrossRefGoogle Scholar
  13. Jiang, F., Li, J., Baoyin, H., Gao, Y. 2009, J. Guidance, Control, Dynamics 32(6), 1827–1837ADSCrossRefGoogle Scholar
  14. Kim, Y.H., Spencer, D.B. 2002, J. Spacecraft Rockets 39(6), 859–865ADSCrossRefGoogle Scholar
  15. Kumar, A., Bera, P., Kumar, J. 2011, Int. J. Thermal Sci. 50(5), 725–735CrossRefGoogle Scholar
  16. Lawden, D.F. 1963, Optimal Trajectories for Space Navigation, Butterworths, LondonzbMATHGoogle Scholar
  17. Lizia, P., Armellin, R., Lavagna, M. 2008, Celestial Mechanics and Dynamical Astronomy 102(4), 335–375CrossRefGoogle Scholar
  18. Mullins, L.D. 1992, J. Astronautical Sci. 40(4), 487–501ADSGoogle Scholar
  19. Park, C., Guibout, V.M., Scheeres, D.J. 2006, J. Guidance, Control, Dynamics 29(2), 321–331ADSCrossRefGoogle Scholar
  20. Tschauner, J., Hempel, P. 1965, Acta Astronautica, 11(2), 104–109Google Scholar
  21. Vaddi, S.S., Alfriend, K.T., Vadali, S.R., Sengupta, P. 2005, J. Guidance, Control, Dynamics 28(2), 262–268ADSCrossRefGoogle Scholar
  22. Yamanaka, K., Ankersen, F. 2002. J. Guidance, Control, Dynamics 25(1), 60–66ADSCrossRefGoogle Scholar
  23. Zanon, D.J., Campbell, M.E. 2006, J. Guidance, Control, Dynamics 29(1), 161–171ADSCrossRefGoogle Scholar
  24. Zhang, J., Tang, G., Luo, Y., Li, H. 2011, Acta Astronautica 68(7-8), 1070–1078ADSCrossRefGoogle Scholar

Copyright information

© Indian Academy of Sciences 2018

Authors and Affiliations

  1. 1.Signal and Image Processing Group, Space Applications CentreAhmadabadIndia

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