Single rotor-base unmanned aerial vehicles (UAVs) represent the most minimalistic design to implement an aerial vehicle. We describe here a mono-rotor UAV, also named mono-spinner, that uses torque modulation (also called swashplateless mechanism) to provide roll and pitch control without the need of a complicated swashplate mechanism. A full non-linear model of the mono-spinner based on the Euler-Poincaré theoretical framework is given including a description of the structure of the drone and its rotor control system. Mechanical properties, kinetic energy and all of the external forces of interest to derive the equations of motion are described. A novel, Lyapunov-stable, quaternion-based nonlinear control law based on the decomposition of the orientation quaternion into a spin component and a reduced orientation component is provided. Finally, simulation results based on parameters measured from a real implementation of a mono-spinner are produced.