cancel
Showing results for 
Search instead for 
Did you mean: 
cancel
Showing results for 
Search instead for 
Did you mean: 

Catenary formula thru ODE

SOLVED
Highlighted
Emerald IV

Catenary formula thru ODE

Can we create the formula of catenary using only Mathcad?

formula.png

 

1 ACCEPTED SOLUTION

Accepted Solutions
Highlighted

Re: Catenary formula thru ODE

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
Highlighted

Re: Catenary formula thru ODE

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

catenary de.jpg

Highlighted

Re: Catenary formula thru ODE

Thanks!

But I think about it

Catenary-Scheme.png

Highlighted

Re: Catenary formula thru ODE

catenary de 1.jpg

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.

Highlighted

Re: Catenary formula thru ODE

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

Highlighted

Re: Catenary formula thru ODE

yes, I vaguely remember.

Highlighted

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

Highlighted

Re: Catenary formula thru ODE

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

Highlighted

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).

Highlighted

Re: Catenary formula thru ODE

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

Highlighted

Re: Catenary formula thru ODE

with old good symbol math

1-Chain-Mathcad-15.png

Highlighted

Re: Catenary formula thru ODE

New formula!!!

1-Chain-Mathcad-Prime-5.png

Announcements