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.