To add to this, the hyperextension you are describing can be done in reverse too. There is a proper machine for it, called, unsurprisingly, the 'reverse hyper' but they are rare.

Here are a couple of videos showing different ways to do it without the machine

https://www.youtube.com/watch?v=Ef4noCz83A4

https://www.youtube.com/watch?v=3d9_W--eUcI

As with the standard hyper. Start slow, good form without any weight.

Give it a try!