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## Catenary formula thru ODE

Can we create the formula of catenary using only Mathcad? 1 ACCEPTED SOLUTION

Accepted Solutions
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## Re: Catenary formula thru ODE

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

Maple Mathcad (full solution in attach - pdf and Prime 6) 12 REPLIES 12
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## Re: Catenary formula thru ODE

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

## Re: Catenary formula thru ODE

Thanks! Highlighted

## Re: Catenary formula thru ODE Highlighted

## Re: Catenary formula thru ODE

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

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## Re: Catenary formula thru ODE

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

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## Re: Catenary formula thru ODE

yes, I vaguely remember.

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## Re: Catenary formula thru ODE

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

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## Re: Catenary formula thru ODE

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

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## Re: Catenary formula thru ODE

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).

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## Re: Catenary formula thru ODE

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

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

## Re: Catenary formula thru ODE

with old good symbol math Highlighted

## Re: Catenary formula thru ODE

New formula!!! 