Numerical Computation of Quasi-Periodic Solutions in the
Circular Restricted 3-Body Problem Based on Percival’s
Variational Principle

There are various solutions to the circular restricted three-body
problem, which is used as a model to describe the movement of
spacecraft. One of the most famous solutions is the periodic orbits
and quasi-periodic solutions that are located near the equilibrium
point on the same line as the main and secondary celestial
bodies. These solutions are advantageous as they can help reduce fuel
consumption while maintaining the spacecraft’s orbit. It is expected
that these solutions will be applied in many missions. In this thesis,
we will first explain a functional that uses Percival’s variational
principle to apply an invariant torus to the circular restricted
three-body problem. We will then use a method to obtain an approximate
quasi-periodic solution by minimizing this functional using the
steepest descent method. Next, we will compare the results obtained
from the proposed method with the ones obtained by numerically
integrating the circular restricted three-body problem. Finally, we
will discuss the prospects of these solutions.