Orthogonal coordinates

In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, orthogonal coordinates are defined as a set of d coordinates 
 
 
 
 
 q
 
 =
 (
 
 q
 
 1
 
 
 ,
 
 q
 
 2
 
 
 ,
 …
 ,
 
 q
 
 d
 
 
 )
 
 
 {\displaystyle \mathbf {q} =(q^{1},q^{2},\dots ,q^{d})}
 
 in which the <a href="/facts/Coordinate_system/Mtd0q4SP">coordinate hypersurfaces</a> all meet at <a href="/facts/Right_angle/psaslRq7">right angles</a> (note that superscripts are <a href="/facts/Einstein_notation/UXwS43wU">indices</a>, not <a href="/facts/Exponent/pac6QY2g">exponents</a>). A coordinate surface for a particular coordinate qk is the <a href="/facts/Curve/xBQ0pTBW">curve</a>, <a href="/facts/Surface/0XA8ce89">surface</a>, or <a href="/facts/Hypersurface/cTvtLVsV">hypersurface</a> on which qk is a constant. For example, the three-dimensional <a href="/facts/Cartesian_coordinate_system/lkTqvMmB">Cartesian coordinates</a> (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 <a href="/facts/Curvilinear_coordinates/RQD7Cajd">curvilinear coordinates</a>.

Orthogonal coordinates open-in-new

Orthogonal coordinates