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Spacecraft Formation Flying by Louis Breger, Jonathan How, Pini Gurfil, Srinivas Rao Vadali, Kyle Alfriend

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7.3 The Gim–Alfriend Geometric Method

The purpose of this section is to derive the state transition matrices for both osculating and mean elements for the relative motion of two neighboring satellites when the reference satellite (chief) is in an elliptic orbit, and both satellites are subjected to the J2si2012_e perturbation. The linear differential equations of relative motion for this system are formidable. A perturbation solution in powers of J2si2013_e could probably be obtained, but there is an easier approach. Rather than solving the equations of motion, the ...

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