Catenary

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Template:Planar curve type

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

Template:Physically definable

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