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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 [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.

Faculty Advisor Name

Jeffrey Knisley

Faculty Advisor Institution

East Tennesee State University

Suggested Mathematics Subject Classification(s)

70F15

Comments

This research was done through a year long Independent Study under the guidance of Dr. Jeff Knisley. Without his knowledge, time, and patience this paper would not have been possible. I am deeply grateful for everything he has done. I would also like to thank Dr. Donald Luttermoser for some LaTeX help.

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Mathematics Commons

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