The GH2 or other small video cameras are very lightweight and the selection for a quality stabilizer are few. Lately, there's been some interest around modifying a Steadicam Smoothee to work with such light cameras. I was able to modify one successfully, but I never got around to showing it's full capabilities. So it's great to see other examples out there, and here's one of the best videos i've seen so far about a modified Smoothee (a.k.a Baby Merlin) with a GH2 camera from Vimeo member MKVideoFilms.
If you want to find out how to modify your own, there's an article posted here: https://cheesycam.com/diy-steadicam-smoothee-mod-cheesycam-baby-merlin/