Del operator in a Cylindrical vector fucntion

  • #1

Main Question or Discussion Point

Hi there
  1. I'm having a hard time trying to understand how come ∂r^/∂Φ = Φ^ ,∂Φ/∂Φ = -r^ -> these 2 are properties that lead to general formula.
  2. I've been thinking about it and I couldn't explain it. I understand every step of "how to get Divergence of a vector function in Cylindrical Coordinates" except for these formulas below.
upload_2018-6-12_1-7-36.png
A picture attached for visualization.
3.
DC-1504v1.png
General formula
Thanks for any help.
 

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  • #2
tnich
Homework Helper
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Hi there
  1. I'm having a hard time trying to understand how come ∂r^/∂Φ = Φ^ ,∂Φ/∂Φ = -r^ -> these 2 are properties that lead to general formula.
  2. I've been thinking about it and I couldn't explain it. I understand every step of "how to get Divergence of a vector function in Cylindrical Coordinates" except for these formulas below.
View attachment 226837 A picture attached for visualization.
3.
View attachment 226838 General formula
Thanks for any help.
If you apply the definition of derivative, these formulas will fall right out. For ##\frac {\partial \hat r} {\partial \theta}##, start with ##\hat r = (cos \theta, sin \theta)##.
By the way, you can easily write ##\hat r## as ##\#\#\backslash hat~r\#\###. For more cool formatting tricks, see the LaTex tutorial.
 

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