If I have a uniform rod
And then I push on each end toward the center
So it bends
What shape does it make? Is it a parabola, a catenary, or something else?
Assume constant stiffness along the rod. I'm using the rod to draw an aerodynamic shape, and I'd like to know what shape I'm drawing. I've read about parabolas and catenaries, but I don't know the answer to this question.