: Matemáticas: orthogonal coordinates

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orthogonal coordinates

In mathematics, orthogonal coordinates are defined as a set of $d$ coordinates ${\\displaystyle \\mathbf {q} =(q^{1},q^{2},\\dots ,q^{d})}$ in which the coordinate hypersurfaces all meet at right angles (note that superscripts are indices, not exponents). A coordinate surface for a particular coordinate $q k$ is the curve, surface, or hypersurface on which $q k$ is a constant. For example, the three-dimensional Cartesian coordinates $(x, y, z)$ is an orthogonal coordinate system, since its coordinate surfaces $x =$ constant, $y =$ constant, and $z =$ constant are planes that meet at right angles to one another, i.e., are perpendicular. Orthogonal coordinates are a special but extremely common case of curvilinear coordinates.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Orthogonal_coordinates)

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