On some extremal relations between inertia tensor elements of a rigid body

It is shown that in course of specific mechanical problem consideration, namely, optimal damping of a spacecraft attitude motion, we need to analyze certain functions of inertia tensor elements of a rigid body. As a result, some general extremal relations were proved. In particular, the product of three inertia moment relative three orthogonal axes is minimal in the case, when these axes are central principal axes of inertia of a rigid body.