natural coordinates

natural coordinates

[′nach·rəl kō′ȯrd·ən·əts]
(fluid mechanics)
An orthogonal, or mutually perpendicular, system of curvilinear coordinates for the description of fluid motion, consisting of an axis t tangent to the instantaneous velocity vector and an axis n normal to this velocity vector to the left in the horizontal plane, to which a vertically directed axis z may be added for the description of three-dimensional flow; such a coordinate system often permits a concise formulation of atmospheric dynamical problems, especially in the Lagrangian system of hydrodynamics.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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Equation for the curve of intersection - natural coordinates. Let us show that the intersection curve of the quadric and the plane is an ellipse.
--"harmonized" system of spherical coordinate ([rho],[??],[[phi]]) connected with natural coordinate system X".
There is, however, one inconvenience: sector-forms are represented in natural coordinates in terms which are not invariant.
Here we define the Chern-Rund connection in natural coordinates as follows:
where [w.sub.i.sup.j] are the components of the connection matrix in natural coordinates. Since the Chern-Rund connection is torsion-free, we can see that (see  and )
We now convert equation 11 from an integral over x-y to an integral in terms of the natural coordinates [xi]-[eta].
We next discuss the transformation from the global X-Y coordinate [integral of] system to a natural coordinate system [xi]-[eta] which has its origin at the center of the element and is scaled so that [xi] and [eta] range between + 1 and - 1.

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