In this paper, a new analytical solution to optimal control problems in formationflying is presented, including the differential gravity effects to the secondorder. The perturbation approach and the calculus of variations are applied tothe optimal control problems in order to obtain an approximate analytical solution.A nonlinear relative dynamics that includes quadratic terms in the differentialgravitational accelerations is used. For the sake of validity, numericalsimulations are performed for satellite reconfiguration cases in which the distancebetween the satellites is large. Finally, the improved accuracy of the newanalytical solution ensuring reasonable fuel usage is confirmed.
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