  Knowledge of the interior density distribution of an asteroid can reveal its
composition and constrain its evolutionary history. However, most asteroid
observational techniques are not sensitive to interior properties. We
investigate the interior constraints accessible through monitoring variations
in angular velocity during a close encounter. We derive the equations of motion
for a rigid asteroid's orientation and angular velocity to arbitrary order and
use them to generate synthetic angular velocity data for a representative
asteroid on a close Earth encounter. We develop a toolkit AIME (Asteroid
Interior Mapping from Encounters) which reconstructs asteroid density
distribution from these data, and we perform injection-retrieval tests on these
synthetic data to assess AIME's accuracy and precision. We also perform a
sensitivity analysis to asteroid parameters (e.g., asteroid shape and orbital
elements), observational set-up (e.g., measurement precision and cadence), and
the mapping models used. We find that high precision in rotational period
estimates (<~0.27 seconds) are necessary for each cadence, and that low
perigees (<~18 Earth radii) are necessary to resolve large-scale density
non-uniformities to uncertainties ~0.1% of the local density under some models.
