I have a goat whose udder swings from side to side when not full when she runs.
I would call it pendulous I believe. It seems to hold it's self up just fine. She's 7 years old, and this is her second year of milking with me without any problems. I told her that if she didn't want her udder swinging back and forth when she runs, that she would have to just not run.
She listened I think, and rarely runs anywhere, so we didn't need the bra after all. (She had ordered the extra heavy duty sports bras like I wear, (but don't need).