Abstract. In this paper we consider the slightly simpler problem of Keplerian motion
restricted to the plane rather than Keplerian motion in three dimensions as done in
\cite[page 11]{GS90}. We parallel the three-dimensional problem in that we use the
same actions to find invariants (integrals) but rather than
working in a six-dimensional phase space to find six independent integrals we restrict
ourselves to a four-dimensional phase space. In doing this, we find that we have
three independent integrals and thus we have a three-dimensional Lie algebra.
Furman University Electronic Journal of Undergraduate Mathematics