Quasi-bielliptic three-body problem

Quasi-periodic Solutions of the Spatial Lunar Three-body Problem

In this paper, we consider the spatial lunar three-body problem in which one body is far-away from the other two. By applying a well-adapted version of KAM theorem to Lidov-Ziglin’s global study of the quadrupolar approximation of the spatial lunar three-body problem, we establish the existence of several families of quasi-periodic orbits in the spatial lunar 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...

Quasi-periodic Solutions of a Spiral Type for Photogravitational Restrict- ed Three-Body Problem

A new type of exact solutions for photogravitational restricted three-body problem (a case of spiral motion) is presented here. A key point is that we obtain the appropriate specific case of spiral motions from the Jacobian-type integral of motion for photogravitational restricted three-body problem (when orbit of small 3-rd body is assumed to be like a spiral). Besides, we should especially no...

Quasi-Periodic Orbits of the Restricted Three-Body Problem Made Easy

A new fully numerical method is presented which employs multiple Poincaré sections to find quasi-periodic orbits. The main advantages of this method are the small overhead cost of programming and very fast execution times, robust behavior near chaotic regions that leads to full convergence for given family of quasi-periodic orbits and the minimal memory required to store these orbits. This meth...