OFFSET
0,1
COMMENTS
This constant separates the parameter ranges of dimensionless tension in determining the shape of the sag curve of a heavy rope into slack solution and tensioned solution.
EXAMPLE
0.41677827980048234921808073511210967457019589611...
MATHEMATICA
RealDigits[x /. FindRoot[Tanh[1/(2*x)] == 2*x, {x, 1/2}, WorkingPrecision -> 100]][[1]] (* Vaclav Kotesovec, Jun 28 2024 *)
PROG
(PARI) my(f(x)=x*cosh(1/(2*x))); solve(x=0.3, 0.5, f'(x))
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Hugo Pfoertner, Jun 27 2024
STATUS
approved