For the gradient in other orthogonal coordinate systems, see Orthogonal coordinates ( Differential operators in three dimensions ).
12.
More general orthogonal coordinates may be obtained by starting with some necessary coordinate surfaces and considering their orthogonal trajectories.
13.
What distinguishes orthogonal coordinates is that, though the basis vectors vary, they are always orthogonal with respect to each other.
14.
Other differential operators can be expressed in the coordinates by substituting the scale factors into the general formulae found in orthogonal coordinates.
15.
Knowing the scale factors, various functions of the coordinates can be calculated by the general method outlined in the orthogonal coordinates article.
16.
Often the metric is diagonal, as is the case for orthogonal coordinates ( see line element ), but not in general curvilinear coordinates.
17.
In an orthogonal coordinate system for a cubic cell, the Miller indices of a plane are the Cartesian components of a vector normal to the plane.
18.
Geometrically they can be lengths along straight lines, or arc lengths along curves, or angles; not necessarily Cartesian coordinates or other standard orthogonal coordinates.
19.
This principle says that in separable orthogonal coordinates, an " elementary product solution " to this wave equation may be constructed of the following form:
20.
For a general inner product space " V ", an orthonormal basis can be used to define normalized orthogonal coordinates on " V ".
