The 3-body problem in Shape Space (3)
Now let's see the how yellow orbit in S evolves according to logarithmic time. It takes an infinite time for the representative point to move away from the initial D=0 configuration, which is therefore pushed back to the infinite past. The point initially moves very slowly, and is then accelerated by the potential well. At the same time friction prevents the point from stabilizing into an elliptic orbit around thee two-body collision point (recall that the only conditions for elliptic orbits are a central force and conservation of energy). The orbits around the two-body collision become smaller and smaller, and the speed of the representative point increases. The two-body collision is reached only asymptotically, at infinite logarithmic time.