Catenary formula thru ODE

[ValeryOchkov]

Can we create the formula of catenary using only Mathcad?

[-MFra-]

Well, it's child's play, just solve the following differential equation, obtained by deriving twice the given function:

[ValeryOchkov]

Thanks!

But I think about it

[-MFra-]

[-MFra-]

but this is a problem of a different nature from the previous one. Now you want the tension in the belt.

[Fred_Kohlhepp]

There were solutions posted years ago based on the fact that the catenary tension is a constant.

[-MFra-]

yes, I vaguely remember.

[tietjee]

The tension has to broken into two forces, horizontal and vertical.  This is for each point along the catenary.  The horizontal force is constant, the vertical force varies along the catenary.  The solution is best solved, for starters, with the lower point being tangent to the x-axis.  This is typical in ship anchor or mooring systems.

Cheers,  David

[-MFra-]

in fact the horizontal component of the tension along the catenary should be constant.

[-MFra-]

The weight of the rope per meter (kg / m) is p, the tension along the catenary  with equation y(x), is: T = p.y(x).

[ValeryOchkov · Accepted solution]

I waited, waited for an answer, and decided to solve this problem myself

Maple

Mathcad (full solution in attach - pdf and Prime 6)

[ValeryOchkov]

with old good symbol math

[ValeryOchkov]

New formula!!!