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 [3, page 11]. 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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East Tennesee State University
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Jason Osborne, A Lie Algebra of Integrals for Keplerian Motion Restricted to the Plane, Furman University Electronic Journal of Undergraduate Mathematics, 5 (2016), 10-22. Available at: http://scholarexchange.furman.edu/fuejum/vol5/iss1/2