Formation flying: Accommodating nonlinearity and eccentricity perturbations
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abstract
Hill-Clohessy-Wiltshire equations describe the relative motion of one satellite with respect to another in a circular reference orbit. Initial conditions that generate periodic solutions to these equations have to be corrected to obtain bounded solutions in the presence of nonlinearity of the differential gravitational acceleration model and eccentricity of the reference orbit. The corrections to the initial conditions due to quadratic terms in the differential gravitational acceleration for circular reference orbits are established first by using a perturbation approach. These corrections are related to the period-matching constraint required for bounded relative motion. Next, the solution to the linear problem including the effect of eccentricity is determined, and a procedure for correcting the along-track bias is presented. The two solutions obtained are combined to produce an asymptotic solution for the quadratic eccentricity problem. The effects of nonlinearity and eccentricity on the relative orbits are characterized as functions of their initial position in the formation.
