See Saw-screen-shot-2018-03-15-20.39.33.png

Hi there, first time here so apologies if this is not the correct thread for this type of question. I hope somebody can help me out! This is a problem I have devised which will serve a purpose in a big chunk of code I am creating for a financial market however I have not done: mechanics, geometry, trig or Pythagoras since secondary school so could do with some help please!

Ok so we have a six-sided see saw (try saying that 6 times quickly), or this can be thought of as a hexagon balancing on a pin. Imagine at the centroid, this see saw can move in any direction (Like brand 1 can freely move in 3 dimensions) [I really hope you can enlarge that JPG file on your side(s).

∑ letís label each brand or Ďseatí: A, B, C, D, E and F.
∑ I have their upforce (labelled AU, BU, CU etc),
∑ their downforce (labelled AD, BD, CD etc),
∑ the length between each seat and the centre (AL, BL, CL etc).
∑ I have the angles between each line (ALBL, BLCL, CLDL etc)

There is no resistance, weight to the see saw, friction or anything else that I remember from mechanics... If thereís anything else you need to know to figure this out, just let me know but I think I have accounted for every aspect required.

The problem
I need an algebraic equation (or rather 6 for a six sided shape such as this one) that explains at what angle Brand 1 will be, away from flat, rest, natural, 180, whatever you want to call it (second equation to show Bís angle, third to show C etc). I imagine this problem will require equations from the realms of mechanics and Mr Pythagoras himself, other than that I am stumped. If anybody is genius enough to figure this out could you please explain it as if you were talking to an advanced toddler.

How does this equation alter if it is a 5 sided shape instead of 6, or 7/8/9??

Any help would be greatly appreciated, I eagerly await your input.