I have seen these videos before, but don’t know how to find them again. Perhaps a space shuttle afficionado can help.
The landings in question would have been pre-1995, so that narrows down the search range.
On one landing, the pilot kept the nose in the air too long after main-gear touchdown; either he was sloppy with the controls or suddenly lost all pitch authority, because the nose gear slammed down on the runway exceptionally hard.
On another landing, the video is from the rear and shows the shuttle undergoing a dramatic fishtail sequence immediately after main-gear touchdown; the rudder swings from one extreme to the other a couple of times, either automatically or under pilot command, in an effort to damp out the oscillations.
Anyone know which missions these were, or how I might find videos of them on YouTube or elsewhere?