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The Lie Algebra sl(2, R) and so-called Kepler-Ermakov Systems

Abstract A recent paper by Karasu (Kalkanlı) and Yıldırım (Journal of Nonlinear Mathematical Physics 9 (2002) 475–482) presented a study of the Kepler‐Ermakov system in the context of determining the form of an arbitrary function in the system which was compatible with the presence of the sl(2, R) algebra characteristic of Ermakov systems and the existence of a Lagrangian for a subset of the systems. We supplement that analysis by correcting some results.