Astronomy and Astrophysics – Astronomy
Scientific paper
Oct 2006
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006cemda..96..137h&link_type=abstract
Celestial Mechanics and Dynamical Astronomy, Volume 96, Issue 2, pp.137-157
Astronomy and Astrophysics
Astronomy
2
Coulomb Thrusting, Rotating Equilibria, Invariant Shape Formation
Scientific paper
In this paper we study shape-preserving formations of three spacecraft, where the formation keeping forces arise from the electric charges deposed on each craft. Inspired by Lagrange’s 3-body problem, the general conditions that guarantee preservation of the geometric shape of the electrically charged formation are derived. While the classical collinear configuration is a solution to the problem, the equilateral triangle configuration is found to only occur with unbounded relative motion. The three collinear spacecraft problem is analyzed and the possible solutions are categorized based on the spacecraft mass-charge ratio. Precise statements on the number of solutions associated with each category are provided. Finally, a methodology is proposed to study boundedness of the collinear solution that is inspired by past understanding and results for the 3-body problem. Given the initial position and the velocity vectors of each craft along with the charges, analytical solutions are provided describing the resulting relative motion.
Hussein Islam I.
Schaub Hanspeter
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