Article ID Journal Published Year Pages File Type
1764830 Advances in Space Research 2013 11 Pages PDF
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.

► Optimality of singular arcs subject to multi-body dynamics are presented. ► Necessary conditions for optimality are explicitly derived and validated. ► They can be considered an expansion of Lawden’s classical results. ► They are practically applied to a non-trivial trajectory optimization problem.

Related Topics
Physical Sciences and Engineering Earth and Planetary Sciences Space and Planetary Science
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