I am working with a system having a massless 2D plane and on that plane there is a rigid object with some mass placed on it. I want to support the plane with wooden sticks such that the system is stable.
You can see that the dotted line is the support polygon (convex hull) made by the support ticks.
Stability for the system can be defined as the Center of mass (CoM) of the object inside the polygon assuming the object is rigid and there is no inclination on the surface.
I want to formulate this problem in a constraint program only using integer values. I am already working on a model and this part is one of the other parts of my model. Hence all my decision variables are integers and as far as I have read, we can formulate polyhedral analysis problems in linear programming.
Problem to tackle: Find the position of 2D n-points such that the system remains stable.
All points are decision variables of the program and are not passed externally
Does anyone here happen to know the formulation in constraint program using only integer variables? Any reading materials you would suggest?