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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!
Attach file Mathcad 15
Solved! Go to Solution.
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.
Here's your symbolic solution Val (though I've used a different notation from your original):
See the attached for the derivation.
Alan
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?
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.