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arXiv · 1402.4402

Ermakov-Lewis Invariants and Reid Systems

Stefan C Mancas·Haret C Rosu
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Abstract

Reid's m'th-order generalized Ermakov systems of nonlinear coupling constant alpha are equivalent to an integrable Emden-Fowler equation. The standard Ermakov-Lewis invariant is discussed from this perspective, and a closed formula for the invariant is obtained for the higher-order Reid systems (m\geq 3). We also discuss the parametric solutions of these systems of equations through the integration of the Emden-Fowler equation and present an example of a dynamical system for which the invariant is equivalent to the total energy

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Stefan C Mancas, Haret C Rosu. 2014-02-18. Ermakov-Lewis Invariants and Reid Systems. https://doi.org/10.1016/j.physleta.2014.05.008

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