# Del Operator for Cylindrical Coordinate

1. Jun 3, 2009

### Harmony

http://img208.imageshack.us/img208/5153/12802868.png [Broken]

Why is the del operator for cylindrical coordinate the upper one and not the lower one? How does the 1/r term arises?

Last edited by a moderator: May 4, 2017
2. Jun 3, 2009

### bartek2009

You could read about general curvilinear coordinates and that should answer your question (plus it will also explain the factors in other expressions from different coordinate systems like e.g. spherical polar coordinates). Basically the unit vectors change with position in cylindrical coordinates and that is why the factor appears.

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Last edited by a moderator: Aug 6, 2009
3. Jun 3, 2009

### tiny-tim

Hi Harmony!

(have a del: ∇ and a theta: θ and a curly d: ∂ )
().eθ has to be the rate of increase per distance in the eθ direction …

but ∂/∂θ is the rate of increase per angle

and distance (in the eθ direction) is r times angle.

4. Jan 22, 2011

### befangler

5. Jan 23, 2011

### befangler

Also, in case the link I provided in my previous post becomes unavailable, PF members arildno and HallsOfIvy walk through the same derivation in another thread here on Physics Forum.

Check it out under Physics Forums>Mathematics>General Math -> Thread = "Del operator with coordinate transformations"