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Optimization of Perturbed Spacecraft Trajectories Using Complex Dual Numbers. Part 1: Theory and Method

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Abstract

The problem of optimization of perturbed trajectories of spacecraft with finite thrust is considered. The problem is solved using an indirect approach based on the application of the necessary optimality conditions in the form of the maximum principle, the continuation method, and complex dual numbers for high-precision calculation of the necessary derivatives of complicated real functions of state variables. The goal of optimization is to calculate trajectories with minimal fuel consumption at a fixed angular distance and free transfer duration. A mathematical model of the spacecraft motion in equinoctial elements with an angular independent variable is used. A mathematical model of the motion, the derivation of the necessary optimality conditions, and a description of the method for solving the problem are given.

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ACKNOWLEDGMENTS

This study was supported by the grant of the Government of the Russian Federation allocated from the Federal Budget for State Support of Scientific Research Conducted under the Guidance of Leading Scientists in Russian Educational Institutions of Higher Education, Research Institutions, and State Research Centers of the Russian Federation (contest 7, resolution no. 220 of the Government of the Russian Federation of April 9, 2010), agreement no. 075-15-2019-1894 of December 3, 2019.

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Authors and Affiliations

  1. Research Institute of Applied Mechanics and Electrodynamics, Moscow Aviation Institute, Moscow, Russia

    V. G. Petukhov

  2. Moscow Aviation Institute, Moscow, Russia

    Sung Wook Yoon

Authors
  1. V. G. Petukhov
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  2. Sung Wook Yoon
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Correspondence to V. G. Petukhov or Sung Wook Yoon.

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Translated by M. Chubarova

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Petukhov, V.G., Sung Wook Yoon Optimization of Perturbed Spacecraft Trajectories Using Complex Dual Numbers. Part 1: Theory and Method. Cosmic Res 59, 401–413 (2021). https://doi.org/10.1134/S0010952521050099

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  • DOI: https://doi.org/10.1134/S0010952521050099

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