Catenary

In deriving the equation of a catenary we turn to the Euler-Lagrange equation: 

\[\frac{d}{dx}\left(\frac {\partial L}{\partial y\prime}\right )= \frac{\partial L}{\partial y}\]

We use this to minimise the potential energy of the hanging object which is an integral. 

The proof that a chain or rope hangs in a cosh shape ($\dfrac{e^x + e^{-x}}{2}$) will follow soon. 

In fact here it is. Write up courtesy of the man Ste. https://docs.google.com/file/d/0B4GMQrQwHpNuXzZ6RzBnMkdnNTQ/edit?usp=docslist_api