Electromagnetic Piston Engine, need to simulate.

I'm working on this project with a group, and we have reached a point were we are lost.

The goal that is trying to be accomplished how is a simulation of the attached picture.

What you looking at is four electromagnets (shown in the deep red) that push and pull the magnet in the center. That force should in turn spin a wheel attached to the magnet.

The motion is very similar to what is shown in these videos:
https://www.youtube.com/watch?v=5kWj_7h1rSY
https://www.youtube.com/watch?v=h0nlACgOwns

What I'm looking to achieve with this thread is how would I go about modelling and simulating in software such as matlab or simulink?

I have been doing research on google, and found nothing that would relate to what I'm trying accomplish. So I'm using the forum to get some better direction.