Def Leppard's Hysteria tour was when they were at the height of popularity and they had the budget to put on a show that would impress. The band decided to put on the concert in the middle of the arena, allowing for all the tickets to be sold in the arena known as in-the-round seating rather then the standard end stage. With Def Leppard at their prime, this allowed the band to sell 3-5,000 tickets more per show.
In-the-round dated back to 1914 when it was first used at Columbia University for plays, but it wasn't until 1978 that a rock band took a stage on tour in the round. Yes developed a rotating stage for its 1978-1979 Tormato tour. The stage was essentially a large record player.
Below is rare 8mm footage of the tour, notice the speed at which the stage turns, begging the question if any of the members got sick.
In this clip filmed during a soundcheck you can get a good luck at all the steel grating that the stage was comprised of.
The stage was hidden from view by a black scrim with the album artwork that was draped all around the stage.
As seen in this video, the scrim would drop at the beginning of the show giving the audience their first glimpse of the impressive stage.
Here is the song Photograph taken from the officially released concert film:
In this MTV segment, there is some great footage and some fans reactions to the stage:
When the arena's the band would play in were too small to fit the entire in-the-round stage setup they simply setup just half of the stage. In this clip filmed at the Hollywood Sportatorium, you can see that setup. This was one of the last ever concerts held at the venue which was notorious for its bad acoustics and fabled rock concerts:
When the band toured American Amphitheaters in the summer of 1988, they used a completely different setup that used pieces of the in-the-round setup but added some stairs on stage left and right and grated steps up to the drum riser. You can get a good look at it during a sound check in this video:
and in concert here: