Variational existence proof for several kinds of periodic orbits
in the planar circular restricted three-body problem
The n-body problem is an important subject in celestial
mechanics. There are many results about periodic orbits of the full
n-body problem using variational methods, but few results in the
restricted three-body problem in this field have been shown. In this
paper, we prove the existence of periodic orbits in the planar
circular restricted three-body problem. We consider the variational
problem under six types of boundary conditions. It is shown that the
action functional under each boundary condition attains the minimum
and we can construct a smooth periodic orbit from each minimizer.

Last modified: Thu Feb 28 11:43:35 JST 2019