Catenoid soap bubbles
11-08-2021, 06:03 PM (This post was last modified: 11-10-2021 11:23 AM by Albert Chan.)
Post: #9
 Albert Chan Senior Member Posts: 2,142 Joined: Jul 2018
RE: Catenoid soap bubbles
At the end of video, Matt showed that bubble collapsed when H/R = 0.66274 ...
Let x = H/r, k = H/R

(R/r) = cosh(H/r) ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ → x/k = cosh(x)

In other words, if k above critical constant (0.66274 ...), equation failed to give a solution.

This is one way to solve for the constant, by geometry

Critical point (at x0) is when cosh(x) tangent line is y = x/k
Matching tangent line, we have:

y = sinh(x0)*(x-x0) + cosh(x0) = sinh(x0)*x + (cosh(x0)-x0*sinh(x0)) = x/k

constant term → x0*tanh(x0) = 1 → x0 ≈ 1.19967864026
linear term ﻿ ﻿ ﻿ ﻿ → sinh(x0) = 1/k﻿ ﻿ ﻿ ﻿ → k ≈ 0.662743419349
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 Messages In This Thread Catenoid soap bubbles - ijabbott - 11-06-2021, 07:51 PM RE: Catenoid soap bubbles - C.Ret - 11-07-2021, 12:11 PM RE: Catenoid soap bubbles - Albert Chan - 11-07-2021, 04:27 PM RE: Catenoid soap bubbles - ijabbott - 11-07-2021, 08:08 PM RE: Catenoid soap bubbles - Albert Chan - 11-08-2021, 01:56 PM RE: Catenoid soap bubbles - Wes Loewer - 11-07-2021, 05:44 PM RE: Catenoid soap bubbles - ijabbott - 11-07-2021, 07:56 PM RE: Catenoid soap bubbles - ijabbott - 11-08-2021, 04:28 PM RE: Catenoid soap bubbles - Albert Chan - 11-08-2021 06:03 PM RE: Catenoid soap bubbles - Joe Horn - 11-09-2021, 02:57 AM RE: Catenoid soap bubbles - ijabbott - 11-09-2021, 08:29 AM

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