Orthogonal Coordinate Systems

  • Thread starter bolbteppa
  • Start date
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Hey guys, I'd really love it if you could post little essays explaining your intuition on how to derive the x, y & z coordinates from all/any of the orthogonal coordinate systems in this list, how you think about, say, bipolar coordinates if you had to re-derive the coordinate system on a desert island etc...

Apart from spherical & cylindrical I have no idea how to remember the others, these two I remember because I can think of the picture & re-derive how to express x, y & z in terms of r, θ & z etc... but the others are completely crazy geometrically & I have no intuition on them, & I need to at least learn how to represent x, y & z in terms of each system (so I can get grad, div, curl etc...) along with intuition on when to use them.

One interesting example of what I'm hoping for is with toroidal coordinates whose wiki is incomprehensible yet apparently there is an insanely simply way (page 114, also in this link) to think about these coordinates, [though the formulas for x, y & z in the links don't agree, which isn't a good sign, apparently they're a bit different but that's not a happy realization :frown:] Thanks!
 
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