#### 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,

In summary, the angular momentum vector is given by the mass moment of inertia tensor times the angular-velocity vector representing the axis of rotation.

Note that the angular momentum vector
does *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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Simple Example

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Relation of Angular to Linear Momentum