An algebraic approach to the minimum-cost multi-impulse orbit transfer problem
Abstract
We present a purely algebraic formulation (i.e. polynomial equations only) of the minimum-cost multi-impulse orbit transfer problem without time constraints, while keeping all the variables with a precise physical meaning. We apply general algebraic techniques to solve these equations (resultants, Gr\"obner bases, etc.) in several situations of practical interest of different degrees of generality. For instance, we provide a proof of the optimality of the Hohmann transfer for the minimum fuel 2-impulse circular to circular orbit transfer problem, and we provide a general formula for the optimal 2-impulse in-plane transfer between two rotated elliptical orbits under a mild symmetry assumption on the two points where the impulses are applied (which we conjecture that can be removed).
Cite
@article{arxiv.1508.02243,
title = {An algebraic approach to the minimum-cost multi-impulse orbit transfer problem},
author = {Martin Avendano and Verónica Martín-Molina and Jorge Martín-Morales and Jorge Ortigas-Galindo},
journal= {arXiv preprint arXiv:1508.02243},
year = {2024}
}
Comments
17 pages, 6 images in 4 figure environments