On 7/15/2013 1:01 PM, Henry Baker wrote:
Ok, so I guess the overall form of the analytic solution will be something like:
PEmin = min(PE_A, PE_B, PE_C, PE_D),
where PE_i = potential energy when vertex i (i=A,B,C,D) is pushed into the middle (where we now have a_planar_ problem, which should be much easier to solve).
In each planar problem, the 'outer' 3 edges are under tension, while the 'inner' 3 edges are under compression.
Make the central vertex the origin.
I guess that the whole thing is linear (at least in terms of displacements), so we should be able to solve the projections onto the X and Y coordinates separately, and then put the results back together again.
Forces are linear, but the energy, which is to be minimized, is quadratic. Brent