  In this article we continue the study of the collapse of three inelastic
particles in dimension $d \geq 2$, complementing the results we obtained in its
companion paper. We focus on the particular case of the nearly-linear inelastic
collapse, when the order of collisions becomes eventually the infinite
repetition of the period $0-1$, $0-2$, under the assumption that the relative
velocities of the particles (with respect to the central particle $0$) do not
vanish at the time of collapse. Taking as starting point the full dynamical
system that describes two consecutive collisions of the nearly-linear collapse,
we derive formally a two-dimensional dynamical system, called the two-collision
mapping. This mapping governs the evolution of the variables of the full
dynamical system. We show in particular that in the so-called Zhou-Kadanoff
regime, the orbits of the two-collision mapping can be described in full
detail. We study rigorously the two-collision mapping, proving that the
Zhou-Kadanoff regime is stable and locally attracting in a certain region of
the phase space of the two-collision mapping. We describe all the fixed points
of the two-collision mapping in the case when the norms of the relative
velocities tend to the same positive limit. We establish conjectures to
characterize the orbits that verify the Zhou-Kadanoff regime, motivated by
numerical simulations, and we prove these conjectures for a simplified version
of the two-collision mapping.
