The three-body problem

Three - Body Problem

A Trilinear Three-Body Problem

In this paper we present a simplified model of a three-body problem. Place three parallel lines in the plane. Place one mass on each of the lines and let their positions evolve according to Newton’s inverse square law of gravitation. We prove the KAM theory applies to our model and simulations are presented. We argue that this model provides an ideal, accessible entry point into the beautiful m...

Effective Interactions for the Three-Body Problem

The three-body energy-dependent effective interaction given by the Bloch-Horowitz (BH) equation is evaluated for various shell-model oscillator spaces. The results are applied to the test case of the three-body problem (H and He), where it is shown that the interaction reproduces the exact binding energy, regardless of the parameterization (number of oscillator quanta or value of the oscillator...

Cross Sections in the Three-body Problem

In Dynamical Systems, Birkho gave a clear formulation of a cross section, suggested a possible generalization to cross sections with boundary, and raised the question of whether or not such cross sections exist in the three-body problem. In this work, we explicitly develop Birkho 's notion of a generalized cross section, formulate homological necessary conditions for the existence of a cross se...

Caustics of the restricted three-body problem

Trajectories of the planar, circular, restricted threebody problem are given in the configuration space through the caustics associated to the invariant tori of quasi-periodic orbits. It is shown that the caustics of trajectories librating in any particular resonance display some features associated to that resonance. This method can be considered complementary to the Poincaré surface of sectio...