Definition:Curvilinear Coordinate System/Examples
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Examples of Curvilinear Coordinate Systems
Polar Coordinates
The canonical example of a curvilinear coordinate system is the polar coordinate system.
Complex Curvilinear Coordinates
Let $u + i v = \map f {x + i y}$ be a complex transformation.
Let $P = \tuple {x, y}$ be a point in the complex plane.
Then $\tuple {\map u {x, y}, \map v {x, y} }$ are the curvilinear coordinates of $P$ under $f$.