Let the pair of three-space coordinates $p_1$ & $p_2$ define a chord between the edges of a cylinder of radius $R_c$ and length $L$. The edges here represent the two circular borders between the smooth surfaces of the cylinder. Let $c_1$ & $c_2$ represent the end-points of the line segment running through the cylinder's center. The goal is to fit a cylinder to this chord such that the conceptual center of mass of the cylinder is positioned as far away as possible from some three-space coordinate $q$. Intuitively, I would expect that this has a unique solution.
We know a few things:
-The distance between points $c_1$ & $c_2$ is, as specified, $L$.
-The distance between points $c_1$ & $p_1$, and $c_2$ & $p_2$ is $R_c$.
-The distance between $c_1$ and $p_2$ is equal to $(L^2 + R_c^2)^\frac{1}{2}$
-The distance between $c_2$ and $p_1$ is likewise equal to $(L^2 + R_c^2)^\frac{1}{2}$
-$R_c$ and $L$ are, of course, $>0$.
My approach thus-far has been to use a symbolic manipulator (Maple and "Reduce" in Mathematica) to find a general expression for $c_1$ & $c_2$ based on these distance relations that I can use to find the cylinder with its mass positioned as far away from the point $q$ as possible. Unsurprisingly, however, my system's memory was exhausted before I could obtain anything useful.
Note! - This is a repost and a slight reformulation of an earlier question I deleted to afford myself some time to try a different approach, and I hope this is not construed as being rude or otherwise disrespectful.