  We introduce a one-dimensional sandpile model which incorporates particle
inertia. The inertial dynamics are governed by a new parameter which, as it
passes through a threshold value, alters the toppling dynamics in such a way
that the system no longer evolves to a self-organized critical state. A range
of mean-field theories based on a kinetic equation approach is presented which
confirm the numerical findings. We conclude by considering the physical
applications of this model, particularly with reference to recent experimental
results.
