TITLE:
Chaos in Planar, Circular, Restricted Three-Body Problem
AUTHORS:
Jan Vrbik
KEYWORDS:
Chaotic Orbits; Perturbation Methods; Three-Body Problem; Resonance
JOURNAL NAME:
Applied Mathematics,
Vol.4 No.1,
January
25,
2013
ABSTRACT:
In this article we analyze the motion of a test particle of a planar, circular, restricted three-body problem in resonance, using the Kustaanheimo-Stiefel formalism. We show that a good qualitative description of the motion can be reduced to three simple equations for semi-major axis, eccentricity and resonance angle. Studying these equations reveals the onset of chaos, and sheds a new light on its weak nature. The 7:4 resonance is used as an example.