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Article
Ermakov Lewis Invariants and Reid Systems
Physics Letters A (2014)
  • Stefan C. Mancas, Embry-Riddle Aeronautical University
  • Haret C. Rosu, Instituto Potosino de Investigacion Cientifica y Tecnologica
Abstract
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.
Keywords
  • Ermakov-Lewis invatiant,
  • Reid system,
  • Emden-Fowler equation,
  • Abel equation,
  • parametric solution
Publication Date
June 13, 2014
DOI
https://doi.org/10.1016/j.physleta.2014.05.008
Citation Information
Stefan C. Mancas and Haret C. Rosu. "Ermakov Lewis Invariants and Reid Systems" Physics Letters A Vol. 378 Iss. 30/31 (2014) p. 2113 - 2117 ISSN: 0375-9601
Available at: http://works.bepress.com/stefan_mancas/3/