Mass second-moment tensor
= Mass second-moment tensor
{title2=$I_{jk}$}
The mass second-moment tensor about a <centre of mass> is $I_{jk}=\int y_jy_k\,dm$. It measures the shape of a mass distribution and appears in <tidal torque theory>. It differs from the mechanical <inertia tensor>, which is $\mathcal I_{jk}=\operatorname{tr}(I)\delta_{jk}-I_{jk}$. For a uniform <ellipsoid> of mass $M$ and semiaxes $a_1,a_2,a_3$, its principal values are $Ma_j^2/5$.