Order and Chaos in Satellite Encounters
In order to describe the motion of two weakly interacting satellites of a
central body we suggest to use orbital elements based on the the linear
theory of Kepler motion in Levi-Civita's regularizing coordinates. The
basic model is the planar three-body problem with two small masses, a model
in which both regular (e.g. quasi-periodic) as well as chaotic motion can occur.
This paper discusses the basics of this approach and illustrates it
with a typical example. First, we will revisit Levi-Civita's regularization
of the two-dimensional Kepler motion and introduce sets of orbital elements
based on the differential equations of the harmonic oscillator. Then, the
corresponding theory for the three-dimensional motion will be developed
using a quaternion representation of Kustaanheimo-Stiefel (KS) regularization;
we present it by means of an elegant new notation.
Download complete paper (25 pages):