### 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.

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Furman University Electronic Journal of Undergraduate Mathematics