Dual-Quaternion-Based Dynamics Modeling for a Rigid–Flexible Coupling Satellite

Dual quaternions can describe both three-dimensional translation and three-dimensional rotation and have the advantages of a simple form, accurate modeling, and precise physical meaning in terms of dynamic modeling. The traditional rigid-body dynamics modeling theory based on dual quaternions is only applicable to the case of modeling for the center of mass. When modeling appendages, the flexible appendages must be symmetrically configured to reduce the modeling complexity. However, in space operations, flexible appendages are usually not symmetrically installed, which significantly limits the applications of dual-quaternion theory. In this paper, we propose a new dual-quaternion derivative rule and a rigid-body dynamic modeling method suitable for any point. The theory can be applied to model flexible appendages with any configuration without changing the mathematical modeling framework. Finally, we demonstrate the integrated dynamic equation of a rigid–flexible coupling system considering the coupling of position and attitude, and we verify the correctness of the model by numerical simulation.