For a diagonal metric tensor , where is the Kronecker delta,
the scale factor for a parametrization , , ..., is defined by
The line element (first fundamental
form) is then given by
The scale factor appears in vector derivatives of coordinates in curvilinear
coordinates.
See also
Curvilinear Coordinates,
Fundamental Forms,
Line
Element,
Metric Tensor
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References
Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, p. 87,
1985.Referenced on Wolfram|Alpha
Scale Factor
Cite this as:
Weisstein, Eric W. "Scale Factor." From
MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ScaleFactor.html
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