I Cylindrical coordinates -Curvilinear

chwala
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Why are the coordinates seemingly used when the symmetry is around ##z## axis? Any particular reason why not ##x## or ##y##. In transforming from Cartesian to cylindrical form; I can see that ##z## is not considered when determining ##r##.
Can we also use ##x## and ##z## assuming that the symmetry is about ##y##? Sorry using phone to type ...will put this into context later. I hope my query is clear enough.
Why are the coordinates seemingly used when the symmetry is around ##z## axis? Any particular reason why not ##x## or ##y##. In transforming from Cartesian to cylindrical form; I can see that ##z## is not considered when determining ##r##.
Can we also use ##x## and ##z## assuming that the symmetry is about ##y##? Sorry using phone to type ...will put this into context later. I hope my query is clear enough.
 
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The directions of the cartesian axes in space are not absolute, but can be chosen to fit the geometry of the particular problem; by convention in axisymmetric geometries the z-axis is placed on the axis of symmetry, giving an obvious extension of plane polar coordinates (x,y) = (r \cos \theta, r \sin \theta).

It is clearly possible to set \begin{split}<br /> x &amp;= w \\<br /> y &amp;= u \cos v \\<br /> z &amp;= u \sin v\end{split}<br /> or \begin{split}<br /> x &amp;= u \sin v \\<br /> y &amp;= w \\<br /> z &amp;= u \cos v \end{split} if you want.
 
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