Reid's mth-order generalized Ermakov systems of nonlinear coupling constant α 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≥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.
Physics Letters A
Scholarly Commons Citation
Mancas, S., & Rosu, H. C. (2014). Ermakov-Lewis Invariants and Reid Systems. Physics Letters A, 378(30/31). https://doi.org/10.1016/j.physleta.2014.05.008