(Catenary) In our Suspension Bridge Cable example we neglected the weight of the cable its...

(Catenary) In our Suspension Bridge Cable example we neglected the weight of the cable itself relative to the weight of the roadbed. At the other extreme, suppose that the weight of the roadbed (or other loading) is negligible compared to the weight of the cable. Indeed, consider a uniform flexible cable, or catenary, hanging under the action of its own weight only, as sketched in the figure. Then Fig. 8 still holds, but with ΛW= μΛs, where y, is the weight per unit arc length of the cable.

(3.1)

Proceeding somewhat as in (10) - (12), derive the governing differential equation