Force distribution to supporting points

[ErikvdW]

Hi everyone!
(little background: I'm trying to develop a small, quick 'n dirty static physics engine to determine whether a stacking of boxes is stable).

If I have a 3D box (with the bottom in the horizontal plane), resting on n points (at [x_n, y_n]), and we apply a downward force F at [x_F, y_F], how can I calculate the resulting forces F_n at these n points?

If the system is in equilibrium then $$\Sigma$$F_n = F.
However, I must also consider that the system might not be in equilibrium (for instance, if all x_n < x_F), so I can't use equilibrium equations. I'd still like to know the forces in that case, though, so that I can calculate the resulting torque.

Is there an easy formula for this?

 

[Naty1]

Seems to me the system will be stable if there is no moment force. So the stacking will be stable when the resultant downward force is between the support points...and unstable if the force is outside any of the support points.

 

[ErikvdW]

Thanks for the reply, but I'm really more interested in the resulting forces than just a stable/not stable decision. For instance, a stair-like stack of three boxes might have the direct weights of each of the boxes between their contact points but might still be unstable because of indirect forces. Which means I need to be able to determine these indirect forces.