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New to the forum (obviously, since this is my first post).

I've been scouring the internet trying to find some guidance on a problem I've been having, but have had no luck. Let me just say first off that my physics and math backgrounds are fairly elementary. I have minors in both areas, but it's been years since I've done anything in them.

The problem I need to solve is the following: Let's say I have an arbitrary polygon. This polygon represents the top-down view of an object. We can assume also that it has no hidden surfaces (all faces of the object are either purely horizontal or purely vertical). I know the location of the vertices (in order), as well as the location of the centre of mass (calculated by triangulating the polygon, averaging the centres of the triangles weighted by their size).

I have X number of people lifting this object, at X different points on its boundary. These points are also known. What I need to figure out is exactly what portion of the weight of the object each person is lifting, based on their positions, assuming a uniform density of the object.

I feel as though, intuitively, this should be a relatively simple thing to calculate, but have had no luck in figuring it out or finding a solution....Could really use some guidance here...

Edit: apologies if this is posted in the wrong place. Mods, feel free to move it if necessary (but it's NOT a homework question)