Recursive dynamics algorithm for multibody systems with variable-speed control moment gyroscopes as actuators

This paper presents a comprehensive recursive formulation of dynamic equations for multibody systems with variable-speed control moment gyroscopes (VS-CMGs). It permits any rigid or flexible body in the system to have a cluster of VS-CMGs in a generic configuration as actuators. The detailed dynamics of the VS-CMGs is taken into consideration to capture the interactions between the VS-CMGs and the flexibilities of the structures. The equations of motion of a flexible body with n VS-CMGs are developed by the Kane's method. The recursive algorithm is obtained through analyzing the kinematics and dynamics between two adjacent bodies, both of which can be rigid or flexible, or one of which is rigid and the other is flexible. The orthonormal complement of the projection matrix of the joint is adopted to express the constraint equations for the structural loops uniformly. Numerical results of an illustrative example are presented to show the accuracy and efficiency of the proposed method by comparing it with a nonrecursive formulation.