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Catenary formula thru ODE

ValeryOchkov
24-Ruby IV

Catenary formula thru ODE

Can we create the formula of catenary using only Mathcad?

formula.png

 

1 ACCEPTED SOLUTION

Accepted Solutions

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

Maple

1-Chain-Maple.png

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

1-Chain-Mathcd.png

View solution in original post

12 REPLIES 12

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

catenary de.jpg

Thanks!

But I think about it

Catenary-Scheme.png

catenary de 1.jpg

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

Fred_Kohlhepp
23-Emerald I
(To:-MFra-)

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

yes, I vaguely remember.

tietjee
14-Alexandrite
(To:Fred_Kohlhepp)

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

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

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).

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

Maple

1-Chain-Maple.png

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

1-Chain-Mathcd.png

with old good symbol math

1-Chain-Mathcad-15.png

New formula!!!

1-Chain-Mathcad-Prime-5.png

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