Illustrating chaos: A schematic discretization of the general three-body problem in Newtonian gravity

Understand

We present a formalism for constructing schematic diagrams to depict chaotic three-body interactions in Newtonian gravity.

• This is done by decomposing each interaction in to a series of discrete transformations in energy- and angular momentum-space.
• Each time a transformation is applied, the system changes state as the particles re-distribute their energy and angular momenta.
• These diagrams have the virtue of containing all of the quantitative information needed to fully characterize most bound or unbound interactions through time and space, including the total duration of the interaction, the initial and final stable states in addition to every intervening temporary meta-stable state.