# Ellipsoid moving on a plane

1. Dec 23, 2009

### burrkie

Ok so basically what I'm trying to model is an ellipsoid on a plane, the planes angle can be changed by the user and the ellisoid should move accordingly. But I have absolutely no idea where to start. I've tried finding equations etc but I could't find anything other than the equation of an ellipse and I have no idea where to go now! Does anyone know what equations I should use or what method I should use or anything?
Seriously stuck and just cannot get my head around how to model it, like should I be using an approximation method or what? ARGH!!

2. Dec 23, 2009

### Staff: Mentor

3. Dec 23, 2009

### burrkie

yes it is but I am trying to break it down, do this first then try and change the shape and the center of gravity etc but for now a simple ellipsoid is what I am aiming for. I've been trying to find equations and such but I've had no luck so I was hoping I might get some more help if I simplified exactly what I need now and see if anyone can help

4. Dec 23, 2009

### Bob S

Look at Poinsot's construction of the torque-free motion of an ellipsoid:
http://en.wikipedia.org/wiki/Poinsot's_construction
Every ellipsoid has 4 independent constants of motion: kinetic energy and three angular momenta about its three principal axes. The result is that the polhode on the inertia ellipsoid rolls on the herpolhode in the invariable plane without slipping.
Bob S

5. Dec 23, 2009

### burrkie

thank you very much this helps a lot. Just reading through it gives me a much better idea of what to do!