A recursive formulation for open-loop gyroelastic multibody dynamics

In this paper,a general recursive formulation of equations of motion is presented for open-loop gyroelastic multibody systems.The gyroelastic multibody system is defined as a multibody system with gyroelastic bodies,whereas a gyroelastic body is composed of a flexible body with a cluster of double-gimbal variable-speed control moment gyroscopes(DGVs).First,the motion equations of a single gyroelastic body are derived using Kane’s method.The influence of DGVs on the static moments,modal momentum coefficients,moments of inertia,modal angular momentum coefficients,and modal mass matrix for a flexible body are considered.The interactions between the DGVs and the flexibilities of the structures are captured.The recursive kinematic relations for a multibody system with different connections are then obtained from a flexible-flexible connection using a transformation matrix.The different connections contain a flexible-flexible connection,which represents a flexible body connecting to another flexible body,flexible-rigid and rigid-rigid connections.The recursive gyroelastic multibody dynamics are obtained by analyzing the kinematics of a multibody system and the dynamics of a single gyroelastic body.Numerical simulations are presented to verify the accuracy and efficiency of the proposed approach by comparing it with a direct formulation based on Kane’s method.