In this paper, we show that nonlinear model predictive control (NMPC) demonstrates excellent performance in driving a reaction wheel pendulum to its unstable equilibrium at which the pendulum is inverted. We show that NMPC is capable of driving the system to this point from the stable equilibrium (i.e. the non-inverted position), often known as `swing-up'. This is as opposed to many common implementations in which two controllers are used - one for swing-up and another for stabilisation or balancing around the equilibrium. We derive an explicit version of the controller which provides a close approximation to the required control input, but can do so within the required sampling period. We demonstrate that this approach generates a real-time controller of a size and speed appropriate for embedded implementation on a microprocessor.