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Existence and Multiple Solutions of the Minimum-Fuel Orbit Transfer Problem

Author

Listed:
  • H. J. Oberle

    (University of Hamburg)

  • K. Taubert

    (University of Hamburg)

Abstract

In this paper, the well-known problem of piloting a rocket with a low thrust propulsion system in an inverse square law field (say from Earth orbit to Mars orbit or from Earth orbit to Mars) is considered. By direct methods, it is shown that the existence of a fuel-optimal solution of this problem can be guaranteed, if one restricts the admissible transfer times by an arbitrarily prescribed upper bound. Numerical solutions of the problem with different numbers of thrust subarcs are presented which are obtained by multiple shooting techniques. Further, a general principle for the construction of such solutions with increasing numbers of thrust subarcs is given. The numerical results indicate that there might not exist an overall optimal solution of the Earth-orbit problem with unbounded free transfer time.

Suggested Citation

  • H. J. Oberle & K. Taubert, 1997. "Existence and Multiple Solutions of the Minimum-Fuel Orbit Transfer Problem," Journal of Optimization Theory and Applications, Springer, vol. 95(2), pages 243-262, November.
    • Handle: RePEc:spr:joptap:v:95:y:1997:i:2:d:10.1023_a:1022627003404
    DOI: 10.1023/A:1022627003404
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    Citations

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    Cited by:

    1. H. Baumann & H. J. Oberle, 2000. "Numerical Computation of Optimal Trajectories for Coplanar, Aeroassisted Orbital Transfer," Journal of Optimization Theory and Applications, Springer, vol. 107(3), pages 457-479, December.
    2. J.B. Caillau & J. Gergaud & J. Noailles, 2003. "3D Geosynchronous Transfer of a Satellite: Continuation on the Thrust," Journal of Optimization Theory and Applications, Springer, vol. 118(3), pages 541-565, September.
    3. Fliege, Jörg & Kaparis, Konstantinos & Khosravi, Banafsheh, 2012. "Operations research in the space industry," European Journal of Operational Research, Elsevier, vol. 217(2), pages 233-240.
    4. M. Cerf, 2013. "Multiple Space Debris Collecting Mission—Debris Selection and Trajectory Optimization," Journal of Optimization Theory and Applications, Springer, vol. 156(3), pages 761-796, March.

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