Define the nominal position vector as expressed in the local level coordinate system rotating with the satellite. The equations of motion are where the dot symbolizes time derivatives and d is the disturbing acceleration. The nonlinear equations of motion can be linearized by assuming the actual location is the nominal location on a circular orbit plus a small perturbation. Then, Equations 2.4-16 and 2.4-17 can be solved to give closed form solutions of the perturbations. If dr = dg = 0, the homogeneous solutions in terms of the initial conditions are Assuming that the solar pressure forces act along the earth-sun line, the disturbances are given by

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