The inclusion of the linearized J2 effect in the Hill equations of relativemotion gives greater insight into satellite formation flying dynamics, and theopportunity to investigate alternative feedback control strategies for thestation keeping task. The work of Schweighart and Sedwick is verified andextended as time varying and analytical models are developed to incorporate theJ2 perturbation and its effects on the relative motion of two or more satellitesin LEO. Analysis is performed in detail to determine the best modelling strategyfor satellite formation keeping in the J2 perturbed environment. The analyticalJ2 model is found to capture relative motion the most accurately, but only givenspecific initial conditions. The time varying model captures leader-followermotion better than the Hill equation and analytical J2 models. LQR control lawsare designed and performance evaluated for the basic Hill equations and the timevarying and analytical J2 models using Matlab/Simulink and the Satellite ToolKit.
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