Methods and apparatus for generating electrical power on aircraft rotor heads are disclosed. The apparatus includes a rotor assembly and a stator assembly. The rotor assembly is rigidly coupled to a rotor head of an aircraft. The rotor assembly is to rotate at a first rate as the rotor head rotates at the first rate. The stator assembly is rotatably coupled to the rotor assembly. The stator assembly includes a stabilizer to aerodynamically resist rotation of the stator assembly. The stabilizer is to cause the stator assembly to rotate at a second rate less than the first rate.