Three classes of Ermakov systems and nonlocal symmetries

TL;DR

This paper explores three classes of Ermakov systems, using algebraic reduction and angular momentum conditions to derive new generalized symmetries, transforming Kepler-Ermakov systems into generalized Ermakov systems.

Contribution

It introduces a simple algebraic reduction process with angular momentum constraints to find novel symmetries in Ermakov systems, including a transformation of Kepler-Ermakov systems.

Findings

Derived new generalized symmetries for three classes of Ermakov systems.

Transformed Kepler-Ermakov systems into generalized Ermakov systems.

Provided a systematic algebraic reduction approach for symmetry analysis.

Abstract

Ermakov systems have attracted enormous treatments in recent times particularly in symmetry analysis. In this paper we consider three classes of the Ermakov systems by using a simple algebraic reduction process with imposed conditions on the magnitude of the angular momentum of each system class to obtain new generalized symmetries. We note that this imposed condition transforms the Kepler-Ermakov systems to the generalized Ermakov systems.