Spherical coordinates

The spherical coordinates ( File:Hepa img1054.gif ) are normally defined in terms of the Cartesian coordinates (x,y,z) by:

The matrix A giving spherical coordinate unit vectors in terms of Cartesian unit vectors ( Coordinate Systems) is then:

The volume element is File:Hepa img1057.gif , and the distance element is File:Hepa img1058.gif .

The above relationships hold when the angle is defined as being with respect to the z axis. It is sometimes convenient to define this angle with respect to the x-y plane, in which case is replaced by File:Hepa img1059.gif and the system becomes left-handed.