up next prev ptail tail

## Article 33The Elastic Catenary.

An elastic string of uniform section and density in its natural state is suspended from two points. Find its equation of equilibrium.

Let the element $d\sigma$ stretch into $ds$; then, by Hooke’s law, , where $\lambda$ is the elastic constant of the string; hence the weight of the stretched element . Accordingly, as before,

which is the intrinsic equation of the curve, and reduces to that of the common catenary when $\mu =0$. The coordinates $x$, $y$ may be expressed in terms of the single parameter $\phi$ by putting

These equations are more convenient than the result of eliminating $\phi$, which is somewhat complicated.

 up next prev ptail top