1. The problem statement, all variables and given/known data Suppose we have a rope of length L and total mass M. Suppose we x its ends at points (xA; yA) and (xB; yB). We want to determine the shape the rope makes, hanging under the influence of gravity. The rope is motionless, with a shape parametrised by y(x) or equivalently, x(y), where x denotes the horizontal coordinate and y the vertical one. We are looking for the shape which minimises the potential energy of the rope. Image below 2. Relevant equations I'm guessing ds = sqrt ( dx^2 + dy^2) can be used. 3. The attempt at a solution Integrate ds over s, and thus it is... integral ds = S [ from Yb to Ya] Xb and Xa would be zero as the horizontal length does not change. As you can see...I'm a bit confused. I don't know how to parametise dx and dy, or can I just use a polar coordinate system?