Quaternion based model for momentum biased nadir pointing spacecraft

Abstract

In this paper, we propose a quaternion based spacecraft model that describes the nadir pointing spacecraft with momentum wheel under gravity gradient torque disturbance. This state space model uses only three components of the quaternion. From this nonlinear model, we derive a linearized state space model for the spacecraft system. We show that unlike all existing quaternion models, this linearized state space model is fully controllable. Therefore, all modern control system design methods can be directly applied to the attitude control system design for momentum biased nadir pointing spacecraft.