Foucault-like properties in the full-body relative spacercraft motion
Keywords:
dual number, dual tensor, six-degree-of-freedom relative orbital motion, spacecraft motionAbstract
The relative orbital motion between the leader and the deputy spacecraft is a six-degree-of-freedom (6-DOF) motion, representing the coupling of the relative translational motion with the rotational one. In recent years, increasing attention has been paid to the modeling of the relative 6-DOF motion of spacecraft. Also, controlling the relative pose of satellite formation is a significant research subject. In this paper, we reveal a real and dual tensor-based procedure to obtain exact expressions for the 6-DOF relative orbital law of motion between two Keplerian confocal orbits. Orthogonal real and dual tensors play a very important role, with the representation of the solution being, to the author knowledge, the shortest approach for describing the complete state onboard solution of the 6-DOF orbital relative motion problem. A representation theorem is provided for the full-body initial value problem. Furthermore, the real and dual parts are split, and representation theorems for relative rotation and translation motions are obtained.
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