  We use a set of simple angular moments to solve the Boltzmann equation in the
relaxation time approximation for a boost invariant longitudinally expanding
gluonic plasma. The transition from the free streaming regime at early time to
the hydrodynamic regime at late time is well captured by the first two-moments,
corresponding to the monopole and quadrupole components of the momentum
distribution, or equivalently to the energy density and the difference between
the longitudinal and the transverse pressures. We relate this property to the
existence of fixed points in the infinite hierarchy of equations satisfied by
the moments. These fixed points are already present in the two-moment
truncations and are only moderately affected by the coupling to higher moments.
Collisions contribute to a damping of all the non trivial moments. At late
time, when the hydrodynamic regime is entered, only the monopole and quadrupole
moments are significant and remain strongly coupled, the decay of the
quadrupole moment being delayed by the expansion, causing in turn a delay in
the full isotropization of the system. The two-moment truncation contains
second order viscous hydrodynamics, in its various variants, and third order
hydrodynamics, together with explicit values of the relevant transport
coefficients, can be easily obtained from the three-moment truncation.
