# Catenary Java Application

## Physics Background

Consider a perfectly flexible but non-elastic filament with some nonzero
mass density. That is, a filament material that can support an infinite tension
along its longitudinal direction without deforming, but no tension at all in
a transverse direction. Ordinary string or rope or cable approximates this
ideal material. Attach two ends of a length of this filament to two supports
and let it dangle. What shape is described by the filament when it reaches
static equilibrium?

If we assume that the only weight acting on the filament is due to the
mass of the filament itself, then a differential equation can be set up to
describe the shape of the dangling filament in two dimentions. (See https://en.wikipedia.org/wiki/Catenary
for details.) The solution of the shape, called a catenary curve, is

where λ is a parameter, and for the length of the filament is

Note that these are transcendental equations in λ, and must be solved
numerically.

(Some think that the catenary is also the curve described by the cables
of a suspension bridge. While of simular shape, the bridge profile is more closely approximated
by a parabola, since the preponderance of the loading on the cable is the weight
of the roadway beneath it. This weight is directed uniformly downward, as opposed
to the case of the free dangling filament, where the weight is only that of the filament
material and thus is along the filament in each differential element.)

## The Catenary Application

Click to Download

Run from a shell or command terminal in the download directory with:

java -jar Catenary.jar

This application lets you adjust the cable length and see its effect on the cable
profile. The solved values of the catenary parameter lambda and the vertical droop
distance of the cable profile are displayed. Note that all dimensions are
in arbitrary distance units. The *x*_{1} coordinate is set to 5 units
for this simulation, so the distance between the towers is 10 units.

Back to Computational Physics Playground page

Back to John Fattaruso's home page