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H
hfeith1-Visitor
1-Visitor
December 17, 2016
Solved

Coordinate system ?

  • December 17, 2016
  • 2 replies
  • 2749 views

Hi,

I' ve the following : https://en.wikipedia.org/wiki/Vibrations_of_a_circular_membrane

I'm sure that this will also work in Mathcad, but, at the moment, I've no idea how to get this thing running

in polar, cylindrical,, or whatever coordinates, to create the same wikipedia animation.

Have you any ideas ?

Thanks in advance.

Best answer by hfeith

Note that the formula in "Vibration of a cylindrical drum.xmcd.zip" was wrong (copy and paste error ). Sorry for that.

I corrcted it. As I had already guessed, it had something to do with

coordinate transformation. I got it now,and from my point of view the case is closed.

Here is the file :

2 replies

W
Werner_E25-Diamond I
25-Diamond I
December 17, 2016

> I'm sure that this will also work in Mathcad

Sure, once you get your math right. But I doubt that anybody will do this for you.

Simply using the last equation in this article and throwing in some arbitrary number obviously doesn't do the job.

H
hfeith1-VisitorAuthorAnswer
1-Visitor
December 29, 2016

Note that the formula in "Vibration of a cylindrical drum.xmcd.zip" was wrong (copy and paste error ). Sorry for that.

I corrcted it. As I had already guessed, it had something to do with

coordinate transformation. I got it now,and from my point of view the case is closed.

Here is the file :

W
Werner_E25-Diamond I
25-Diamond I
December 29, 2016

Much better 😉

But it should be simply u instead of sin(u) as we are dealing with cylindrical coordinates, not spherical ones.

You can also let Mathcad do the transformation by using the appropriate argument in CreateMesh:

H
hfeith1-VisitorAuthor
1-Visitor
December 29, 2016

cyl2xyz didn't work, first, though I decided to transform "manually".

The cylindrical coordinates transform is of course the correct one.

In the formula for Mathcad I also replaced J0(...) by Jn(m,...).to do

justice to the general case.

Have a nice day.

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