Coordinate systems. Derivatives

  • #1

Main Question or Discussion Point

## \vec{r}=\rho \cos \varphi \vec{i}+\rho \sin \varphi \vec{j}+z\vec{k} ##
we get
[tex]\vec{e}_{\rho}=\frac{\frac{\partial \vec{r}}{\partial \rho}}{|\frac{\partial \vec{r}}{\partial \rho}|}[/tex]
[tex]\vec{e}_{\varphi}=\frac{\frac{\partial \vec{r}}{\partial \varphi}}{|\frac{\partial \vec{r}}{\partial \varphi}|}[/tex]
Is it correct for any orthogonal system or maybe for any system? Why you can use this relation?
 

Answers and Replies

  • #2
mathman
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It would help if you would define the symbols, [tex]\vec{e}_{\varphi}, \vec{e}_{\rho}[/tex]
 
  • #3
Unit vectors in cylindrical system.
 
  • #4
mathman
Science Advisor
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If you divide any vector by its magnitude you get a unit vector. I am not sure what you are asking?
 

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