Asphericity

Asphericity is defined as (Eq.5):

$⟨A⟩=\frac{⟨{\mathrm{T}\mathrm{r}}^2-3M⟩}{⟨{\mathrm{T}\mathrm{r}}^2⟩}$

where $\mathrm{T}\mathrm{r}$ is the trace of the moment of inertia tensor, given by (Eq. 3)

$\mathrm{T}\mathrm{r}=R_1^2+R_2^2+R_3^2$

and $M$ is the sum of the three minors, given by

$M=R_1^2{R}_2^2+R_1^2{R}_3^2+R_2^2{R}_3^2$

where $R_1^2$, $R_2^2$ and $R_3^2$ are the three eigenvalues of the tensor. $⟨A⟩$ ranges from 0 for a spherical structure (or any of the platonic solid structures), to 1.

See also

• Radius of gyration
• Random walk