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)



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.

Included in

Mathematics Commons



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.