  The stability for all generic equilibria of the Lie-Poisson dynamics of the
$\mathfrak{so}(4)$ rigid body dynamics is completely determined. It is shown
that for the generalized rigid body certain Cartan subalgebras (called of
coordinate type) of $\mathfrak{so}(n)$ are equilibrium points for the rigid
body dynamics. In the case of $\mathfrak{so}(4)$ there are three coordinate
type Cartan subalgebras whose intersection with a regular adjoint orbit give
three Weyl group orbits of equilibria. These coordinate type Cartan subalgebras
are the analogues of the three axes of equilibria for the classical rigid body
in $\mathfrak{so}(3)$. In addition to these coordinate type Cartan equilibria
there are others that come in curves.
