LINEAR STATE-SPACE MODELS FOR J2-PERTURBED SATELLITE RELATIVE MOTION
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This paper presents the derivations of linear differential equations for modeling perturbed satellite relative motion dynamics. In the first part of this paper a linear model is obtained for the evolution of the relative motion in a rotating Cartesian coordinate system. This model is developed using expressions for the secular drift rates and the short-period variations of the orbital elements of the reference satellite. The secular in-track linearization error of the model for the case of a mean circular orbit is shown to be consistent with its analytical estimate for the unperturbed problem. The relative state linearization errors for eccentric orbits show reasonable growth rates. The second part of the paper derives a nonhomogeneous linear model in a curvilinear coordinate system. The second model, simplified for the circular reference orbit, is shown to capture more of the nonlinear effects than does the relative Cartesian coordinate model.
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