How do I calculate the tensor of inertia of a non-rigid body?

How do I calculate the tensor of inertia of a rotating non-rigid body? Is the usual formula:

$$T_{ij} = \int{\rho( x_ix_j - \delta_{ij} x^kx_k)d^3x}$$

still correct?

• $\rho(\vec{x})$ – Eli Jan 24 at 13:19
• @Eli what does it mean? That the density is not a constant, but the whole formula is still valid? – mattiav27 Jan 24 at 13:39