POV Parkour Videos

[Alzran]

So, this summer I worked at a camp. My boss had a Go Pro Hero 2 and let me borrow it to get some footage.
That said, I managed to get some fairly decent POV footage of my training (considering my ability level at the time). However, I also noticed the video turned out really shaky because of all the movement.

MY FOOTAGE:
FIRST:


SECOND: (copy/paste to your URL bar)
youtube.com/watch?v=cZ9a3RCq-6Y



This next one is not my footage, but notice how smooth the camera is. No doubt it is still a go pro, but I am curious how I can go about software-editing my footage to look smooth like this.

(copy/paste to your URL bar)
youtube.com/watch?v=j-mEnMMmSrQ