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Optimal Space Trajectories with Multiple Coast Arcs Using Modified Equinoctial Elements

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  • Mauro Pontani

    (Sapienza University of Rome)

Abstract

The detection of optimal trajectories with multiple coast arcs represents a significant and challenging problem of practical relevance in space mission analysis. Two such types of optimal paths are analyzed in this study: (a) minimum-time low-thrust trajectories with eclipse intervals and (b) minimum-fuel finite-thrust paths. Modified equinoctial elements are used to describe the orbit dynamics. Problem (a) is formulated as a multiple-arc optimization problem, and additional, specific multipoint necessary conditions for optimality are derived. These yield the jump conditions for the costate variables at the transitions from light to shadow (and vice versa). A sequential solution methodology capable of enforcing all the multipoint conditions is proposed and successfully applied in an illustrative numerical example. Unlike several preceding researches, no regularization or averaging is required to make tractable and solve the problem. Moreover, this work revisits problem (b), formulated as a single-arc optimization problem, while emphasizing the substantial analytical differences between minimum-fuel paths and problem (a). This study also proves the existence and provides the derivation of the closed-form expressions for the costate variables (associated with equinoctial elements) along optimal coast arcs.

Suggested Citation

  • Mauro Pontani, 2021. "Optimal Space Trajectories with Multiple Coast Arcs Using Modified Equinoctial Elements," Journal of Optimization Theory and Applications, Springer, vol. 191(2), pages 545-574, December.
    • Handle: RePEc:spr:joptap:v:191:y:2021:i:2:d:10.1007_s10957-021-01867-2
    DOI: 10.1007/s10957-021-01867-2
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    References listed on IDEAS

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    1. Bruce A. Conway, 2012. "A Survey of Methods Available for the Numerical Optimization of Continuous Dynamic Systems," Journal of Optimization Theory and Applications, Springer, vol. 152(2), pages 271-306, February.
    2. Mauro Pontani & Bruce Conway, 2014. "Optimal Low-Thrust Orbital Maneuvers via Indirect Swarming Method," Journal of Optimization Theory and Applications, Springer, vol. 162(1), pages 272-292, July.
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