Weighted catenary


A weighted catenary is a catenary curve, but of a special form. A "regular" catenary has the equation
for a given value of a. A weighted catenary has the equation
and now two constants enter: a and b.

Significance

A catenary arch has a uniform thickness. However, if
  1. the arch is not of uniform thickness,
  2. the arch supports more than its own weight,
  3. or if gravity varies,MathOverflow: , accessdate: April 13, 2017
it becomes more complex. A weighted catenary is needed.
The aspect ratio of a weighted catenary describes a rectangular frame containing the selected fragment of the curve theoretically continuing to the infinity.
arch: fat at the bottom, skinny at the top.

Examples

The Gateway Arch in the American city of St. Louis is the most famous example of a weighted catenary.
Simple suspension bridges use weighted catenaries.

General links