Thursday, March 15, 2018

Is the Equilibrium Curve a Catenary?


  Although the parametric equations for the equilibrium curve involve the linear mass density, the fits for A and B don't appear to be affected by changes in the value for the linear mass density, λ. All the  values for the minimum agree to 15 decimal places.


At the minimum gλs+B=0 so B=-g λsmin making the argument of the sinh-1u equal to u=gλ(s-smin)/A so there are two parameters, A/gλ and smin appear to be independent.


What we've been calling the equilibrium equations may in fact be the parametric equations for a catenary.

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