  The levitation of a macroscopic object within a superconducting resonator
provides a unique and novel platform to study optomechanics, quantum
information, and gravitational wave detection. Existing mirror-method and
single-loop models for calculating magnet levitation are insufficient for
predicting the position and motion of the levitated magnet. If the
cavity-magnet interaction is modeled using a large number of smaller surface
current loops, one can quantitatively model the dynamics of the levitation of
the magnet within the cavity. The magnet's most-likely position and orientation
can be predicted for non-trivial cavity geometries and cavity orientations.
Knowing the potential energy landscape within the cavity configuration also
provides a means to estimate the resonant mechanical frequencies at which the
levitated magnet vibrates, and enables tailoring the cavity design for specific
outcomes.
