  We calculate the effective long-term convective velocity and dispersive
motion of an ellipsoidal Brownian particle in three dimensions when it is
subjected to a constant external force. This long-term motion results as a
"net" average behavior from the particle rotation and translation on short time
scales. Accordingly, we apply a systematic multi-scale technique to derive the
effective equations of motion valid on long times. We verify our theoretical
results by comparing them to numerical simulations.
