How'd they do that U2 Video?

Factual Questions
1

This has been bothering me for years: U2’s “Even Better than the Real Thing” video - How’d they do the flying camera work?

For those it hasn’t seen it, the band (one at a time) stand on a stage and perform the song. The camera does a dizzying crane like shot: It rotates around them: overhead, underneath, in a smooth complete circle around them. There is no track or apperatus in the shot. The only clue to how the trick is done, is that they’re standing on what looks to be a slotted stage, i.e. Bono straddles the shallow hole in the stage.

I used to think that it was on some arm that was cranked and since you never saw the camera make a complete loop, it only made a partial loop around the band. However, I just watched it again and sure enough, there is a couple instances where the camera makes a full loop around Bono. This is driving me batty, help?

2

I seem to remember reading at the time that they actually were on a complete looping track, but the tracks were digitally removed from the completed film. I wouldn’t swear by my memory of this, but it makes sense.

3

Can you confirm it? If it’s true, I feel like a complete poop flinging monkey. I was thinking of some sort of mechanical apparatus, but that makes so much sense. GRRR…