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
Recommended Citation
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: https://scholarexchange.furman.edu/fuejum/vol5/iss1/2
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.