What is the relationship between the UH60 Blackhawk stabilator function lateral sideslip and pitch coupling?
The sideslip to pitch coupling is a result of the canted tail rotor and the asymmetry of the main rotor downwash. The tail rotor thrust pushes the tail to the right and upward (pitch down). The main rotor downwash across the tail boom also generates a pitch up motion.  The 'static' position of the stabilator is set (stab range is 10 deg up to 45 deg down based on airspeed) to counter this pitch tendency.  

A right sideslip condition will result in a reduction of tail rotor vertical thrust resulting in a pitch up motion. The stabilator is programmed downward to counter the pitch up. Conversely a left sideslip will result in increased tail rotor vertical thrust and a pitch down motion.  In this case the stabilator will be programmed up to counter the downward pitch.