Second mass moment tensor
= Second mass moment tensor
{title2=$I_{ij}=\int \rho(\mathbf x)x_ix_j\,d^3x$}
The second mass moment tensor records the quadratic spatial distribution of mass. Its trace-free part is the <mass quadrupole moment> $Q_{ij}=I_{ij}-\delta_{ij}I_{kk}/3$. The mechanical moment-of-inertia tensor instead equals $J_{ij}=\delta_{ij}I_{kk}-I_{ij}$. A rigid rotation $L$ transforms the second mass moment tensor as $I(t)=L(t)I(0)L(t)^T$.