Inverse Transformation of Elliptical Relative State Transition Matrix
2014
A new set of relative
orbit elements (ROEs) is used to derive a new elliptical formation flying model
in previous work. In-plane and out-of-plane relative motions can be completely
decoupled, which benefits elliptical formation design. In order to study the
elliptical control strategy and perturbation effects, it is necessary to derive
the inverse transformation of the relative state transition matrix based on
relative orbit elements. Poisson bracket theory is used to obtain the linear
transformations between the two representations: the relative orbit elements
and the geocentric orbital frame. In this paper, the details of these
transformations are presented.
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