Modeling Relative Motion Using Orbital Elements
This chapter establishes a methodology for obtaining arbitrary high order approximations to the relative motion between spacecraft by utilizing the Cartesian configuration space in conjunction with classical orbital elements. The chapter proposes utilizing the known inertial expressions describing vehicles in elliptic orbits in order to obtain a time-series representation of the motion in a rotating frame, where the coefficients of the time series are functions of the orbital elements. It is shown that under certain conditions, this time-series becomes a Fourier series. The chapter presents high-order approximation which provides important insights into boundedness and commensurability ...
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