Necessary conditions for the optimality of singular arcs of spacecraft trajectories subject to multiple gravitational bodies

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4 Citations (Scopus)

Abstract

This document analyzes the optimality of intermediate thrust arcs (singular arcs) of spacecraft trajectories subject to multiple gravitational bodies. A series of necessary conditions for optimality are formally derived, including the generalized Legendre-Clebsch condition. As the order of singular optimality turns out to be two, an explicit formula for the singular optimal control is also presented. These analytical outcomes are validated by showing that they are identical to Lawden's classical result if the equations of motion are reduced for a central gravity field. Practical utility is demonstrated by applying these analytical derivations to a candidate optimal trajectory near the Moon subject to solar and Earth perturbation. While the candidate optimal trajectory turns out to be bang-singular-bang, the intermediate thrust arc satisfies all the necessary conditions for optimality.

Original languageEnglish
Pages (from-to)2125-2135
Number of pages11
JournalAdvances in Space Research
Volume51
Issue number11
DOIs
Publication statusPublished - 2013 Jan 1

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spacecraft trajectories
Spacecraft
spacecraft
arcs
trajectory
Trajectories
thrust
trajectories
Moon
optimal control
gravity field
moon
Equations of motion
Gravitation
equations of motion
derivation
Earth (planet)
perturbation
gravitation

All Science Journal Classification (ASJC) codes

  • Aerospace Engineering
  • Space and Planetary Science

Cite this

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title = "Necessary conditions for the optimality of singular arcs of spacecraft trajectories subject to multiple gravitational bodies",
abstract = "This document analyzes the optimality of intermediate thrust arcs (singular arcs) of spacecraft trajectories subject to multiple gravitational bodies. A series of necessary conditions for optimality are formally derived, including the generalized Legendre-Clebsch condition. As the order of singular optimality turns out to be two, an explicit formula for the singular optimal control is also presented. These analytical outcomes are validated by showing that they are identical to Lawden's classical result if the equations of motion are reduced for a central gravity field. Practical utility is demonstrated by applying these analytical derivations to a candidate optimal trajectory near the Moon subject to solar and Earth perturbation. While the candidate optimal trajectory turns out to be bang-singular-bang, the intermediate thrust arc satisfies all the necessary conditions for optimality.",
author = "Chandeok Park",
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T1 - Necessary conditions for the optimality of singular arcs of spacecraft trajectories subject to multiple gravitational bodies

AU - Park, Chandeok

PY - 2013/1/1

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N2 - This document analyzes the optimality of intermediate thrust arcs (singular arcs) of spacecraft trajectories subject to multiple gravitational bodies. A series of necessary conditions for optimality are formally derived, including the generalized Legendre-Clebsch condition. As the order of singular optimality turns out to be two, an explicit formula for the singular optimal control is also presented. These analytical outcomes are validated by showing that they are identical to Lawden's classical result if the equations of motion are reduced for a central gravity field. Practical utility is demonstrated by applying these analytical derivations to a candidate optimal trajectory near the Moon subject to solar and Earth perturbation. While the candidate optimal trajectory turns out to be bang-singular-bang, the intermediate thrust arc satisfies all the necessary conditions for optimality.

AB - This document analyzes the optimality of intermediate thrust arcs (singular arcs) of spacecraft trajectories subject to multiple gravitational bodies. A series of necessary conditions for optimality are formally derived, including the generalized Legendre-Clebsch condition. As the order of singular optimality turns out to be two, an explicit formula for the singular optimal control is also presented. These analytical outcomes are validated by showing that they are identical to Lawden's classical result if the equations of motion are reduced for a central gravity field. Practical utility is demonstrated by applying these analytical derivations to a candidate optimal trajectory near the Moon subject to solar and Earth perturbation. While the candidate optimal trajectory turns out to be bang-singular-bang, the intermediate thrust arc satisfies all the necessary conditions for optimality.

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