Compact unmanned aerial vehicles (UAVs) for confined and cluttered spaces are constrained by the exposed, high-speed rotors of conventional multirotors, which are fragile on contact and hazardous near people or obstacles. This paper develops a monocopter, a single-rotor craft that fuses lift and propulsion in one structure, in which propulsion is achieved through a fully integrated electric ducted fan (EDF) and four aerodynamic fins placed within the fan’s exhaust for stabilization. A control-oriented dynamic model is derived from first principles using an energy-based Euler-Lagrange formulation, presented in the manipulator form standard for rotorcraft attitude dynamics and specialized to the single-fan and fin-stabilized configuration. The full configuration-dependent inertia and Coriolis matrices are obtained, and the equivalent body-frame equations expose the gyroscopic coupling that dominates the transverse dynamics. A stability analysis establishes the oblate-inertia condition that governs whether the vehicle’s natural, uncontrolled rotation is stable, then the model is linearized about the spin equilibrium for control, and a four-fin allocation provides three-axis control together with reaction-torque cancellation under a Proportional-Integral-Derivative law on a commercial flight control stack. Simulation reproduces the gyroscopic precession and fin-damped recovery of the spinning body and the deterministic hover spin equilibrium, and an indoor proof-of-concept demonstration confirms that the fabricated prototype hovers with a stable, upright attitude under fin stabilization, the continuous body spin being characterized separately in open loop.