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Scale Factor -- from Wolfram MathWorld

  • ️Weisstein, Eric W.
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For a diagonal metric tensor g_(ij)=g_(ii)delta_(ij), where delta_(ij) is the Kronecker delta, the scale factor for a parametrization x_1=f_1(q_1,q_2,...,q_n), x_2=f_2(q_1,q_2,...,q_n), ..., 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.

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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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