Inertia Ellipsoid -- from Eric Weisstein's World of Physics

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Inertia Ellipsoid

Let

where is the unit vector along the rotation axis of a rotating body, written componentwise as , then

where I is the moment of inertia tensor and its components. Also define

then

This can be transformed to the principal axes such that

which is the inertia ellipsoid.

Moment of Inertia, Moment of Inertia Tensor