Oh my god! Someone who understands relativity! It's a MIRACLE! I love you...
I mean, what?
Oh, how it retains stability? I don't see why it wouldn't. Firstly, keep in mind how HUGE this "disc" is. It's gargantuan. Secondly, obviously since the rest of the universe is being accelerated by the same force (presumably), the UA must pass the Earth along its sides as well, and thus isn't necessarily being pushed from the bottom like a wave, but rather being carried along as if with a current. Thus, the stability is pretty much assured unless turbulence was hit, but since we're in free space, I don't know what kind of torrents we would run into that could knock such a massive disc out of orientation.
~D-Draw