Parallel axis theorem: Difference between revisions

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=== Tensor generalization ===

The parallel axis theorem can be generalized to calculations involving the [[Moment of inertia#Inertia tensor|inertia tensor]]<ref name="Abdulghany">A. R. Abdulghany, American Journal of Physics 85, 791 (2017); doi: https://dx.doi.org/10.1119/1.4994835 .</ref>. Let {{math|''I_ij''}} denote the inertia tensor of a body as calculated at the centre of mass. Then the inertia tensor {{math|''J_ij''}} as calculated relative to a new point is

:<math>J_{ij}=I_{ij} + m\left(|\mathbf{R}|^2 \delta_{ij}-R_i R_j\right),</math>