Dynamics of flexible multibody systems with variable-speed control moment gyroscopes

This paper presents a generic global matrix formulation for the dynamics of flexible multibody systems with variable-speed control moment gyroscopes (VSCMGs). The flexible bodies are assumed to exhibit only small deformation, and they are connected in a tree topology by hinges permitting large rotation and translation. A cluster of VSCMGs is mounted on each body for actuation; it is assumed that the VSCMGs are statically and dynamically balanced, and their rotors are axisymmetric. A minimum set of dynamic equations are derived systematically via a mixed use of Kane's method and Newton-Euler equations. The parameters of each flexible body are augmented to take into account the inertias of the attached VSCMGs. Moreover, a skew-symmetric gyroscopic matrix and three control-input-mapping matrices are defined to represent the passive and the active gyroscopic torques of the VSCMGs in a global matrix manner. Three examples are given to show the usefulness, versatility, and correctness of the proposed formulation. As an additional contribution, also presented are linear dynamic equations for a spacecraft with flexible appendages and embedded VSCMGs.