Abstract
M.Sc.
Important ideas from dynamical systems theory and the restricted three-body
problem are introduced. The intention is the application of dynamical systems
theory techniques to the restricted three-body problem to better understand the
phenomenon of gravitational capture.
Chapter 1 gives a much deeper review of the purpose of this dissertation.
Chapter 2 introduces and reviews important concepts from dynamical systems.
Chapter 3 reviews the restricted three-body problem and all important aspects
of the problem.
In chapter 4 we define and study the phenomenon of gravitational capture.
We take a novel approach by applying a symplectic method, namely the implicit
midpoint method, to model trajectories in the restricted three-body problem.
As far as we know, this is the first time such a method has actually been applied,
with other authors preferring to apply explicit methods in trajectory modelling.
In the closing of this chapter we review our whole discourse and suggest topics
for future research.
The disseration is concluded with two appendix chapters. In the first chapter
we list all the computer code we have written for this dissertation. The second
appendix chapter reviews the n-body problem and we show a full solution of
the two-body problem.