More commonly used is a model based on spherical trigonometry formulae. These formula call for entering the latitude and longitude of the observing location, precisely leveling the base, then finding stars using an accurate clock. I use the model popularized by Taki. He uses a matrix of directional cosines to convert between telescope and celestial coordinates. The telescope pointing values are calculated from the telescope's altitude and azimuth, and time at the moment the object is precisely centered in the field of view.
Drift is caused by pointing errors.
Positions to track to, or, velocities to track by, are calculated based on assumptions of how the telescope is aligned to the sky. Inaccuracies in this alignment will cause the object to appear to slowly drift away from the center of the field. Centering the object, then pressing a button on the hand paddle, causes drift to be calculated and automatically adopted. Use drift nulling to precisely track an object for long exposure imaging on CCDs or film. Drift will slowly change as the telescope tracks for hours into a new portion of the sky.