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.
Highlights
An alternative method to study the dynamics of elliptical formation flying based on a new set of relative orbit elements was presented
To make the ROE-based method more understandable, it is necessary to derive the transformations between the two representations: the relative orbit elements and the geocentric orbital frame
The control laws can be obtained from the inverse matrix of the relative state transition matrix (Table 1)
Summary
An alternative method to study the dynamics of elliptical formation flying based on a new set of relative orbit elements was presented. Other transformations were used by Garrison et al [2] to obtain the equations of the relative motion for an elliptical reference orbit. Using Alfriend’s method, called geometric method, Gim [4] introduced J2 perturbations and Sengupta introduced second order effects [5] This solution has none of the drawbacks of Hill and Lawden equations. It can take into account second order effects, eccentric reference orbit, and perturbations. In order to analyze the perturbation effects and the control strategy, the inverse transformation of relative state transition matrix is greatly needed. The inverse transformation of the relative state transition matrix is obtained to analyze the perturbation effects and control strategy in the third section.
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