Secular Instability in the Three-Body Problem

High inclination orbits in the secular quadrupolar three-body problem

The Lidov-Kozai mechanism (Kozai 1962; Lidov 1962) allows a body to periodically exchange its eccentricity with inclination. It was first discussed in the framework of the quadrupolar secular restricted three-body problem, where the massless particle is the inner body, and later extended to the quadrupolar secular nonrestricted three body problem (Harrington 1969; Lidov & Ziglin 1976; Ferrer & ...

Global instability in the elliptic restricted three body problem∗

The (planar) ERTBP describes the motion of a massless particle (a comet) under the gravitational field of two massive bodies (the primaries, say the Sun and Jupiter) revolving around their center of mass on elliptic orbits with some positive eccentricity. The aim of this paper is to show that there exist trajectories of motion such that their angular momentum performs arbitrary excursions in a ...

Correlation of macroscopic instability and Lyapunov times in the general three-body problem

We conducted extensive numerical experiments of equal mass three-body systems until they became disrupted. The system lifetimes, as a bound triple, and the Lyapunov times show a correlation similar to what has been earlier obtained for small bodies in the Solar System. Numerical integrations of several sets of differently randomised initial conditions produced the same relationship of the insta...

Three - Body Problem

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...