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24-Ruby IV

Catenary formula thru ODE

Can we create the formula of catenary using only Mathcad?

ACCEPTED SOLUTION

Accepted Solutions
24-Ruby IV
(To:-MFra-)

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
21-Topaz II
(To:ValeryOchkov)

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

24-Ruby IV
(To:-MFra-)

Thanks!

21-Topaz II
(To:ValeryOchkov)

21-Topaz II
(To:ValeryOchkov)

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

23-Emerald I
(To:-MFra-)

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

21-Topaz II
(To:Fred_Kohlhepp)

yes, I vaguely remember.

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

21-Topaz II
(To:Fred_Kohlhepp)

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

21-Topaz II
(To:ValeryOchkov)

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).

24-Ruby IV
(To:-MFra-)

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

Maple

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

24-Ruby IV
(To:ValeryOchkov)

with old good symbol math

24-Ruby IV
(To:ValeryOchkov)

New formula!!!

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