Re: Catenary determined by two points and length

In article <457862fb$0$5766$edfadb0f@xxxxxxxxxxxxxxxxxxxx>, Louise
<no@xxxxxxx> wrote:

I found a solution for the catenary curve in an earlier post


http://groups.google.dk/group/sci.math/browse_thread/thread/3d1e48a3b6c86e9d/6
1e9e01c119b387c?lnk=st&q=catenary+length&rnum=1&hl=da#61e9e01c119b387c

but in the end, calculation of parameter 'a' is required as

2 a sinh[L/(2a)] = sqrt(s^2 - h^2)

How to do that?


One can simplify, a little bit...
.... but only a bit.

Let L/2a = x

Let (1/L)sqrt*s^2 - h^2) = m

Then

sinh(x) = mx.

If m > 1 then there is a unique positive x satisfying this equation.
But I don't think there is much chance of expressing it in terms of any
well-known function. Numerical solution is feasible.

--
Chris Henrich
http://www.mathinteract.com
God just doesn't fit inside a single religion.
.

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