  The behaviour of the lower order moments of the velocity distribution
function for a system of inelastic granular disks driven by vertical vibrations
is studied using a kinetic theory. A perturbative kinetic theory for
vibro-fluidised beds was proposed by Kumaran (JFM, v. 364, 163). A scheme to
generalise this theory to higher orders in the moments is presented here. With
such a method it is possible to obtain an analytical solution to the moments of
the distribution function up to third order.
