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.