#### Angular Momentum Vector in Matrix Form

The two cross-products in Eq.(B.19) can be written out with the help of the vector analysis identity^{B.23}

where

The matrix is the Cartesian representation of the

*mass moment of inertia tensor*, which will be explored further in §B.4.15 below. The vector angular momentum of a rigid body is obtained by summing the angular momentum of its constituent mass particles. Thus,

*not*in general point in the same direction as the angular-velocity vector . We saw above that it does in the special case of a point mass traveling orthogonal to its position vector. In general, and point in the same direction whenever is an

*eigenvector*of , as will be discussed further below (§B.4.16). In this case, the rigid body is said to be

*dynamically balanced*.

^{B.24}

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