Rotational motion control of a spacecraft

This note describes a systematic procedure for the control synthesis of a rigid spacecraft using the energy shaping method. The geometric concept of a mechanical system in a coordinate-independent form is used to derive a control algorithm for the Euler-Poincare equations. The main result of this note is a specialization of the method on the unit quaternion group. This note is concluded with the examples of the potential functions and implementation for the three-axis attitude control problem.