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has been cited by the following article:

• TITLE: Inverse Transformation of Elliptical Relative State Transition Matrix

  AUTHORS: Jianfeng Yin, Yinrui Rao, Chao Han

  KEYWORDS: Relative Orbit Elements, Elliptical Formation Flying, Relative State Transition Matrix, Inverse Transformation, Poisson Bracket

  JOURNAL NAME: International Journal of Astronomy and Astrophysics, Vol.4 No.3, August 14, 2014

  ABSTRACT: 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.