  According to Newton's law of gravitation the force between two particles
depends upon their inertial, as well as their active and passive gravitational
masses. For ordinary matter all three of these are equal and positive. We
consider here the more general case where these quantities are equal in
magnitude for a given particle but can differ in sign. The resulting set of
possible interactions allows each particle type to be assigned to one of
precisely four different classes, and the results of N-body simulations show
that the corresponding dynamics can give rise to a fairly rich spectrum of
possible outcomes, some of which are familiar from nature at various scales.
Total energy and momentum are conserved by all of these interactions if the
definitions of momentum and kinetic and potential energy are suitably
generalised.
