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Radius of Gyration


A positive number k such that a lamina or solid body with moment of inertia about an axis I and mass m is given by

 I=mk^2.

Pickover (1995) defines a generalization of k as a function R_g quantifying the spatial extent of the structure of a curve and given by

 R_g=(sqrt(int_0^inftyr^2p(r)dr))/(2int_0^inftyp(r)dr),

where p(r) is the length distribution function. Small compact patterns have small R_g.


See also

Moment of Inertia, Radius of Curvature, Radius of Torsion

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References

Pickover, C. A. Keys to Infinity. New York: Wiley, pp. 204-206, 1995.

Referenced on Wolfram|Alpha

Radius of Gyration

Cite this as:

Weisstein, Eric W. "Radius of Gyration." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RadiusofGyration.html

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