Analytical Model of Eddy Currents in a Reaction Sphere Actuator

A recently proposed technique to control the satellite attitude using a magnetically levitated sphere requires the development of suitable models of its dynamics. One of the phenomena that can affect motion of the system are eddy currents induced in the stator of the actuator due to time variable magnetic field generated by rotational motion of a permanent magnet rotor. We present an analytical model of the eddy currents for the actuator with eight-pole rotor. The model is derived using a second-order vector potential-based approach, and the solution is obtained in terms of spherical harmonic functions. This model allows us to study rotor rotations with constant angular frequency around an axis arbitrarily oriented with respect to both rotor and stator of the reaction sphere actuator.