INVARIANT SHAPE SOLUTIONS OF THE SPINNING THREE CRAFT COULOMB TETHER PROBLEM

摘要

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. We give a description of the physical model of the formation and its equations of motion. Inspired by Lagrange's three body problem, we derive general conditions that guarantee preservation of the geometric shape of the formation. We show that while the classical collinear configuration is a solution to the problem, the equilateral triangle configuration is not. For collinear configurations, not any three spacecraft formation with arbitrary charges will qualify as a solution. Hence, we analyze the three collinear spacecraft problem and categorize the solutions based on the spacecraft mass-charge ratio. We give precise statements on the number of solutions associated with each category. Finally, we propose a methodology to study boundedness of the collinear solution that is inspired by past understanding and results for the three body problem. Studying boundedness of the collinear formation is the subject of current research.