I know the basic equation of a catenary is
y = a*cosh((x-x0)/a)+b
Length of a catenary curve is
L = a*sinh((x-x0)/a)
where x0 is a symmetry point or vertex or lowest x co-ordinate of a curve.
I can reverse manipulate using this length equation.
The small length Ln = (total length - length at a particular point)
Ln = a* [ sinh((x_start-x0)/a) - sinh((x_n-x0)/a) ]
where x_start is the starting point at one end of a catenary x_n is the x co-ordinate at length Ln (small fixed length along the curve)
In this equation I know all the terms except x_n and hence I would like to rewrite this equation of the form xn = other terms.
I am unable to reverse this equation as I am not sure how to remove sinh in the equation, can anyone please suggest me a way to do it.