Spurious terms in the three-body problem

Different Types of attractors in the Three Body Problem perturbed by dissipative Terms

We study the evolution of a conservative dynamical system with three degrees of freedom, where small non conservative terms are added. The conservative part is a Hamiltonian system, describing the motion of a planetary system consisting of a star, with a large mass, and of two planets, with small but not negligible masses, that interact gravitationally. This is a special case of the three body ...

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...

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...

The Spurious Path Problem in Abstraction

Abstraction is a powerful technique in search and plan-ion is a powerful technique in search and planning. A fundamental problem of abstraction is that it can create spurious paths, i.e., abstract paths that do not correspond to valid concrete paths. In this paper, we define spurious paths as a generalization of spurious states. We show that spurious paths can be categorized into two types: sta...