### Volume 5, 1999. 10 - 22. Jason Osborne

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