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

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2.5 Non-Keplerian Motion and Orbital Perturbations

The solutions in Section 2.3 were obtained for the nominal, undisturbed Keplerian motion. When perturbations act upon the body, the motion is no longer Keplerian. In order to solve for the resulting non-Keplerian motion, Euler [56] and Lagrange [57] have developed the variation-of-parameters (VOP) procedure, a general and powerful method for the solution of nonlinear differential equations. Before applying this method to non-Keplerian motion, we will illustrate it in the next subsection.

2.5.1 Variation of parameters

In essence, the VOP method suggests to turn the constants of the unperturbed motion, resulting from the homogenous solution of a given differential equation, into functions of time. ...

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