Orbit-attitude-structure coupled modelling method in local translational coordinate frame for multibody systems

Abstract

The absolute coordinate-based (ACB) method, including absolute nodal coordinate formulation and natural coordinate formulation, is a widely-used dynamic modelling method for multibody systems. However, the problem of accuracy loss would arise when multi-scale motions are described in the same global coordinate system, such as large-scale orbital motions, small-scale attitude motions and structural vibrations, and micro-scale contact/collision. To address this problem, an ACB method in local translational coordinate system is proposed such that the large-scale orbital motions can be separated from other smaller-scale motions. The dynamic equations are derived by the Hamilton's equations and the Kronecker product. The validity of the proposed method is studied using an orbit-attitude coupled model of an orbiting rigid plate. It is found that the attitude errors of the original ACB method increase as time step size decreases. The reason for this counterintuitive phenomenon is that more serious accuracy loss is encountered for smaller time step size. In addition, more iterations are required for the original ACB method to obtain the prescribed tolerable error in each time step due to accuracy loss. In comparison, the proposed method is more accurate and efficient in numerical simulations. Finally, the proposed method is applied to the orbit-attitude-structure coupled simulation of a space robotic system.