The 3-body problem in Shape Space (2)

Let's compare the Newtonian decription with the one on S, for now in Newtonian time.

The dynamics starts near a 2-body collision, which in Newtonian terms corresponds to one of the particles being very far from the others. The distant particle moves towards the others, the moment of inertia is decreasing and the dilatational momentum is negative, but increasing in time.  The representative point emerges from the  potential well in S, as the third body gets closer to the Keplerian pair (red curve).
3-body Shape Space3-body Shape Space
When the representative point on S has climbed out of the potential well, the pair is destroyed and a three-body dynamics dominates for a short (Newtonian) time. During this phase the dilatational momentum reaches 0, and the logarithmic Shape time encounters a coordinate singularity.
The arrow of time is reversed here, and the yellow curve starts. A new Keplerian pair is formed, in this case between the same two particles as before, meaning that the yellow curve sinks into the same potential well the red curve came out of. The isolated particle flies away and the Keplerian pair become increasingly isolated, with a dynamics that becomes increasingly more energy-preserving.
As the moment of inertia keeps growing indefinitely, the representative point in S falls ever more deeply into its potential well.

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