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Minimum-Time Continuous-Thrust Orbit Transfers

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Abstract

To solve the minimum-time orbital transfer problem under continuous thrust, initial values of the Lagrange costates are required in the calculus of variations formulation. Assuming circle-to-circle transfer, expressions are developed for the approximate values of the optimal initial costates, which are then used as starting guesses for the associated two-point boundary value problem. The optimal initial costates are modeled as functions of the thrust and final radius in canonical units. These approximations work for noncircular destination orbits, as well as for noncoplanar transfers. Examples are provided for coplanar and noncoplanar orbital transfers. A dynamic step limiter is also presented which improves convergence in the shooting method.

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Authors and Affiliations

  1. Major, United States Air Force, Department of Aeronautics and Astronautics, Graduate School of Engineering, Air Force Institute of Technology/ENY, Wright-Patterson Air Force Base, 45433, OH, USA

    James D. Thorne

  2. Department of Aeronautics and Astronautics, Graduate School of Engineering, Air Force Institute of Technology/ENY, OH, 45433, Wright-Patterson Air Force Base, USA

    Christopher D. Hall (Assistant Professor of Aerospace and Systems Engineering)

  3. Space and Missile Center/MTDG, CA, 90245, Los Angeles Air Force Base, USA

    James D. Thorne

  4. Department of Aerospace and Ocean Engineering, Virginia Polytechic Institute and State University, VA, 24061, Blacksburg, USA

    Christopher D. Hall (Assistant Professor of Aerospace and Systems Engineering)

Authors
  1. James D. Thorne
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  2. Christopher D. Hall
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Thorne, J.D., Hall, C.D. Minimum-Time Continuous-Thrust Orbit Transfers. J of Astronaut Sci 45, 411–432 (1997). https://doi.org/10.1007/BF03546400

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  • DOI: https://doi.org/10.1007/BF03546400

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