CATENARY
Problem (Modification of SIAM Review, June 1995, pg 224-229)
Consider three similar rods, each of length one foot, are hinged end to end to form one long flexible chain. The ends are attached to two different points at the same height which are 2 feet apart. The chain will swing initially but will come to rest in a position with the least potential energy. We choose our axes so that the y axis points up and the ends of the chain are at (0,0) and (2,0).