Modified Initial Conditions for Periodic Relative Motion of Satellite Formation Flying
by
Zhang Chenguang
Department of Precision Instruments and Mechanology, Tsinghua University, Beijing, China
Coauthors: Chen Darong

Satellite formation flying draws much attention in space technology. In this paper, two sets of initial conditions leading to periodic relative motion are obtained, which improve the initial conditions gained from the Hill-Clohessy-Wiltshire(HCW) equations.

By using the perturbation method, the initial conditions produced by the HCW equations are modified in order to reduce formation dispersing. For circular reference orbit, the analytical solutions of the HCW equations perturbed by a small parameter are obtained, which capture the third order nonlinear items. A secular term is isolated from the analytical solutions. By choosing proper initial values of the perturbed equations, a set of modified initial conditions for HCW equations are proposed. These initial conditions are adapted to projected circular formation and general circular formation. For small eccentricity reference orbit, by keeping the second order nonlinear items and expanding the eccentricity to its first item, another set of modified initial conditions for various formations is obtained, which also eliminates the secular term to keep close formations.

Date received: April 27, 2008