Is the catenary the trajectory of anything? Notice that the parabola, defined by certain properties, is also the trajectory of a cannon ball. Does the same sort of thing hold for the catenary? That is, is the catenary, defined by certain properties, also the trajectory of something?

From the right perspective, maybe.

![enter image description here](

(image from Wikipedia)

I'm not exactly sure how to frame this as a trajectory problem, but certainly there is stuff moving and a catenary is traced!

We have a square moving horizontally at a constant speed, and rotating at "the right" constant angular velocity (I'm not certain the angular velocity is fixed, but I suspect it is). Throughout a given quarter rotation starting with a vertex of the square at the bottom, the point directly below the radius will trace out an inverted catenary.