Definition:Curvilinear Coordinate System/Cartesian Representation

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Definition

The relation between curvilinear coordinates and Cartesian coordinates can be expressed as:

\(\ds x\) \(=\) \(\ds \map x {q_1, q_2, q_3}\)
\(\ds y\) \(=\) \(\ds \map y {q_1, q_2, q_3}\)
\(\ds z\) \(=\) \(\ds \map z {q_1, q_2, q_3}\)


\(\ds q_1\) \(=\) \(\ds \map {q_1} {x, y, z}\)
\(\ds q_2\) \(=\) \(\ds \map {q_2} {x, y, z}\)
\(\ds q_3\) \(=\) \(\ds \map {q_3} {x, y, z}\)


where:

$\tuple {x, y, z}$ denotes the Cartesian coordinates
$\tuple {q_1, q_2, q_3}$ denotes their curvilinear equivalents.


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