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Optimal bounded-thrust space trajectories based on linear equations

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Abstract

Necessary and sufficient conditions for solution of the general minimum-fuel linear bounded-thrust spacecraft trajectory problem are presented in terms of fundamental matrix solutions and their inverses. This work is rigorous, generalizes and unifies many known results for specific problems, and also presents a new necessary condition. Finally, an application is presented for a spacecraft rendezvous near a general Keplerian orbit in which the linearized equations of motion are nonautonomous. A fundamental matrix solution is found and inverted, solving this class of problems.

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Communicated by D. G. Hull

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Carter, T.E., Brient, J. Optimal bounded-thrust space trajectories based on linear equations. J Optim Theory Appl 70, 299–317 (1991). https://doi.org/10.1007/BF00940628

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Key Words

  • Optimization of linear systems
  • optimal space trajectories
  • bounded thrust
  • fuel optimal trajectories
  • orbital rendezvous
  • linear equations of motion
  • Keplerian orbits