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## Can we solve it symbolical?  24-Ruby III

## Can we solve it symbolical?

There is a chain on the wall. What should be its length S so that the force F is minimal.
Below is one of the numerical solutions of the problem.
Is it possible to find an analytical solution. Not 1.258 but one expression!  1 ACCEPTED SOLUTION

Accepted Solutions  16-Pearl
(To:ValeryOchkov)

The equation I supplied is about as far as one can reasonably go symbolically.  The equation tanh(k) = 1/k doesn't have a closed form analytical solution as far as I know, so further calculations must be done numerically.

4 REPLIES 4  16-Pearl
(To:ValeryOchkov)

Here's your symbolic solution Val (though I've used a different notation from your original): See the attached for the derivation.

Alan  24-Ruby III
(To:AlanStevens)

Thanks, Alan!

If the equation coth(k) = k has not the symbolical solution than our problem about optimal chain has not the symbolical solution.

True?  16-Pearl
(To:ValeryOchkov)

The equation I supplied is about as far as one can reasonably go symbolically.  The equation tanh(k) = 1/k doesn't have a closed form analytical solution as far as I know, so further calculations must be done numerically.  24-Ruby III
(To:AlanStevens)

Is this one kay for the solving our problem?  