Sequential Design of Satellite Formations with Invariant Distances
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This paper presents a general sequential methodology to design a cluster of satellites with constant intersatellite distance. The orbits are assumed to be Keplerian with small eccentricity. The motion of the satellites, with respect to the orbital reference frame, is obtained by linearizing the kinematic equations and is expressed in terms of relative orbital elements. The key idea presented in this paper consists of eliminating the mean anomaly dependence from the expression of the intersatellite distance. Three distinct cases are analyzed depending on the relative orbits: 1) same plane, 2) with same relative orbit center, and 3) other cases. The procedure consists of sequentially solving two quadratic constraint equations for each additional satellite. This sequential approach allows the design of clusters with a large number of satellites. This paper also shows that a time-invariant plane can be associated with each cluster; thus, simplified constraint equations, involving the relative orbital parameters, can be obtained. Finally, the proposed design methodology is clarified with examples highlighting the time-invariant rigidity of the cluster. Copyright 2011 by the American Institute of Aeronautics and Astronautics.
