Converting arbitrary Cartesian vector to cylindrical

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Discussion Overview

The discussion revolves around the conversion of a vector from Cartesian coordinates to cylindrical coordinates, specifically focusing on the components of the vector V={Vx,Vy,Vz}. Participants are exploring the process and implications of this conversion, including cases where certain components may be zero.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant expresses uncertainty about how to start the conversion process from Cartesian to cylindrical coordinates.
  • Another participant questions the conversion process specifically when the z component is zero.
  • A different participant suggests that if Vz=0, it would remain zero after conversion, indicating a lack of transformation for that component.
  • Another participant points out that the conversion can be recognized as a transformation from Cartesian coordinates (x, y) to polar coordinates, with cylindrical coordinates extending this to include the z component.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the conversion process, and there are multiple viewpoints regarding the treatment of the z component and the nature of the transformation.

Contextual Notes

Some participants express confusion about the initial steps of the conversion and the implications of having a zero z component, indicating potential gaps in understanding the transformation process.

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Hello PF, I have a problem to solve in the following form: Given a vector with Cartesian components, V={Vx,Vy,Vz}, find its components in circular cylindrical coordinate.

Given the actual vector components, it'd be very easy to convert. But I have no idea where to start on this. Any guide to where to start from will be much appreciated!
 
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If the z component were zero then what kind conversion would it be?
 
Well, its a cylindrical coordinate, so Vz wouldn't go over any transformation, right? So if Vz=0, then after the conversion it will still be 0. I am still very lost...
 
I was hoping you'd recognize it as a conversion from x,y to polar coordinates. Cylindrical are an extension of polar to 3D by adding the z component.
 

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