Catenary

Definition

Cartesian and parametric equations

The Cartesian equation for the catenary is:

$y=\alpha \cosh(x/\alpha )$

where $\alpha$ is a parameter determining how much the catenary opens up.

Physical definition

The catenary is described as follows: it is the shape taken by a hanging flexible wire under the influence of uniform gravitational force, when supported at the ends. Here, the downward direction gravitationally corresponds to the negative $y$-axis, and the parameter $\alpha$ is related to the extent of gravitational force.

Constructs

A surface of revolution corresponding to this planar curve is: catenoid