Divergence in cylindrical coordinate system

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Discussion Overview

The discussion centers on the derivation of the divergence formula in cylindrical coordinates, focusing on specific aspects of the unit vector derivatives as presented in a referenced paper. Participants seek clarification on the mathematical expressions and concepts involved in this derivation.

Discussion Character

  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion regarding the derivatives of unit vectors in cylindrical coordinates, specifically \frac{\partial\hat{\rho}}{\partial\phi} = \hat{\phi} and \frac{\partial\hat{\phi}}{\partial\phi} = \hat{\rho}.
  • Another participant suggests referring back to the first page of the paper for clarification on the derivation of unit vectors with respect to the coordinates.
  • A participant reiterates their confusion and seeks further assistance on how to express \overline{}\rho in terms of Cartesian coordinates, indicating difficulty in formatting their question.
  • One reply points out that the information regarding the unit vectors can be found on page 1 of the referenced link.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus, as confusion remains regarding the specific mathematical details of the divergence formula and the unit vector derivatives. Multiple viewpoints on how to approach the problem are present.

Contextual Notes

Participants reference specific pages in the paper for clarification, indicating that the discussion may depend on the definitions and explanations provided therein. There is an indication of unresolved mathematical steps related to the differentiation of unit vectors.

Sesse
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I am trying to understand the derivation of the divergence formula in cylindrical coordinates. www.csupomona.edu/~ajm/materials/delcyl.pdf paper does a good job of explaining it but I don't understand 2 things that the author does.
\frac{\partial\hat{\rho}}{\partial\phi} = \hat{\phi} and \frac{\partial\hat{\phi}}{\partial\phi} = \hat{\rho}
Derivation is on page 3.
Can anyone help me understand this?
 
Last edited by a moderator:
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go back to page 1: "derivation of unit vectors with the coordinates"
 
Sesse said:
I am trying to understand the derivation of the divergence formula in cylindrical coordinates. www.csupomona.edu/~ajm/materials/delcyl.pdf[/URL] paper does a good job of explaining it but I don't understand 2 things that the author does.
[tex]\frac{\partial\hat{\rho}}{\partial\phi} = \hat{\phi}[/tex] and [tex]\frac{\partial\hat{\phi}}{\partial\phi} = \hat{\rho}[/tex]
Derivation is on page 3.
Can anyone help me understand this?[/QUOTE]

As note below, one finds z^ etc (unit vector), in variation vectors does the differentiation with respect to [tex]\rho[/tex],[tex]\phi[/tex], z

OK
Now my question is how do you find

[tex]\overline{}[/tex][tex]\rho[/tex] (line above, could not get that to work)= x [tex]\widehat{}[/tex]x+ y [tex]\widehat {}[/tex]y
 
Last edited by a moderator:
that one is found in page 1 of the link
 

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