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One more catenary

ValeryOchkov
24-Ruby IV

One more catenary

Do you know an analytical solution of this problem - a closed chain on the horisontal cylinder?

Mathcad Prime 5 two sheets (Find & Minimize) in attach.

1-Schema.png

2-Functions.png3-Input-PE.png4-Minimize.png

5-Itog.png

 

1 ACCEPTED SOLUTION

Accepted Solutions

11 REPLIES 11

One more try with Mathcad 15

Close сhain with pendant on the cylinder

7-G.png

Order for the analytical solution of the closed chain problem on a cylinder

Order.pngOrder-1.pngOrder-2.pngOrder-3.png

OR! No symbolic solution with catenary 🤔

May be there is one symbolic solution for this problem - a parabola, not a catenary!

Parabola.png 

The graphical solution of the problem.

The function (the symbolic solution) needed!  

1-Schema.png6a-Plot.png

One pseudo analytical solution

See What is the better function for this curve? 

6b-CKO.png

Solution

6a-Plot-1.png

6b-CKO-1.png

I published an article about a chain on a cylinder in the article collection of the Institute of Mechanics of Moscow University. This institute employs people who calculated the flights of the first spacecraft - Sputnik, Jury Gagarin etc!

See please attach!


@ValeryOchkov wrote:

Russian version of te article


You mean English version. Thanks!

Yes! English!

Thanks to all for the help!

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