Internal forces in an isolated system I did a weird activity and now I am trying to figure out the physics behind it:
While sitting on a chair I kept my feet above the ground and tried to move the chair forward. I was able to. Initially, I thought that perhaps the center of mass won't be changing as I was pushed backwards. But I moved the chair for a while and saw that it had moved a considerable distance and I was still sitting on the chair. Hence the center of mass did change for sure. According to Newton's second law, there must be an external force acting on the system(me and the chair). But I am not able to figure out what force is it. I have a feeling that it is somewhere related to the fact that the system is not completely isolated but I am not sure how.   
Note:
I am not in contact with the ground or any other object close to me. I have lifted my feet and have my hands on my lap.
 A: The movement you are performing is similar to hopping or jumping - see diagram below. It is much more difficult when you sit on the chair than when you stand, because you do not have as much flexibility, but it is essentially the same kind of movement. You could do even better by standing on the chair and tying it to your feet, then jumping on the chair as you would on the ground.

Using your arms (instead of your legs) as springs, you squat in the chair (b) then suddenly push yourself up and forward, dragging the chair with you when your arms are extended. It is slightly more effective if you hold yourself upright first (a) then swoop down before pushing all in the same movement. Swinging your legs also helps - when jumping you swing your arms and push with your legs; in the chair you swing your legs and push with your arms.  
You could think of the chair as shoes - you push the ground through them, and because they are tied to your feet they leave the ground with you when you jump.
There are external forces acting here - you and the chair are not an isolated system. Contact forces with the ground - friction and normal reaction - as well as inertia/momentum, are essential - you cannot perform this kind of movement in space or when floating in water. You have to push down and back on the ground in order to get the ground to push upward and forward on you. 
A: This is an interesting question.
First of all, your human body is not a rigid system. So basically while you are attempting to do this act, you can observe that different portions of your body move in different directions or creating a small wave. While trying to move the chair forward, your upper body moves forward then the pulls your lower  body towards it, now, the real question is where does the upper body get that support from to pull the lower body? 
Here comes inertia into play. When you jerk your upper body, it resists moving till a certain amount of time, this is inertia's role. So what you are basically doing is you are by jerking your body in that fashion, you are harvesting the force of inertia and using that to move the chair. This resistance exist's only till a limited amount of time or till your body is trying to accelerate itself because that is inertia's nature. Try to move a longer distance in a single wave, that might help you getting a better perception of it.
Hope that helps.
A: I don't think Astro Jes's answer really answers the question. The energy obviously comes from the OP's body. However friction plays a big role here. 
As the body moves to store up "forward energy" it moves slowly backwards and the friction between the chair and the floor holds the chair/person system in a fixed position. In other words the chair stays in place. However when the body is thrust forward quickly, then the forward momentum of the body/chair system overcomes the friction and the whole system moves forward. 
The point is that if the chair/floor contact was frictionless, then moving forward wouldn't be possible. 
A: I respect MaxW's view. But the term that he is calling the forward energy is what I am calling inertia's role. The reason for me to answer again is that he has neglected inertia's role completely and is stating that friction is the only reason for such movements and is also stating that this movement is not possible without friction, which is the only point I'm disagreeing to. 
Because, in a twisting machine we have ball bearings, and so the friction is almost negligible. So, how does this movement happen?

I think this should explain the dominance of inertial force in such cases.
My only notion for answering again is to highlight the facts and nothing else.
Hope this helps. 
