Asphericity: Difference between revisions
Carl McBride (talk | contribs) m (Added range) |
Carl McBride (talk | contribs) m (Added an internal link) |
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<math>\langle A \rangle </math> ranges from 0 for a spherical structure (or any of the platonic solid structures), to 1. | <math>\langle A \rangle </math> ranges from 0 for a spherical structure (or any of the platonic solid structures), to 1. | ||
==See also== | ==See also== | ||
*[[Radius of gyration]] | |||
*[[Random walk]] | *[[Random walk]] | ||
==References== | ==References== | ||
<references/> | <references/> | ||
[[category: classical mechanics]] | [[category: classical mechanics]] | ||
Latest revision as of 16:49, 18 March 2014
Asphericity is defined as [1] (Eq.5):
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \langle A \rangle = \frac{\langle \mathrm{Tr}^2 -3M \rangle }{\langle \mathrm{Tr}^2 \rangle}}
where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathrm{Tr}} is the trace of the moment of inertia tensor, given by (Eq. 3)
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathrm{Tr} = R_1^2 + R_2^2 + R_3^2}
and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle M} is the sum of the three minors, given by
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle M= R_1^2R_2^2 + R_1^2R_3^2 + R_2^2 R_3^2}
where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R_1^2} , Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R_2^2} and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R_3^2} are the three eigenvalues of the tensor. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \langle A \rangle } ranges from 0 for a spherical structure (or any of the platonic solid structures), to 1.