NIGERIAN JOURNAL OF SCIENCE AND ENVIRONMENT
Journal of the Faculties of Science and Agriculture, Delta State University, Abraka, Nigeria
ISSN: 1119-9008
DOI: 10.5987/UJ-NJSE
Email: njse@universityjournals.org
REMARKS ON NONLOCAL SYMMETRIES AND ERMANNO-BERNOULLI CONSTANTS FOR REDUCING SOME DYNAMICAL SYSTEMS
DOI: 10.5987/UJ-NJSE.17.107.1 | Article Number: C143D216 | Vol.11 (1) - September 2012
Author: Arunaye F. I.
Keywords: Nonlocal symmetry, Reduction process, Laplace-Runge-Lenz vectors, Ermanno- Bernoulli constants, Dynamical systems
In the consideration of nonlocal symmetries of the dynamical system
·x· + gr 1
x + hr18 = 0
it was shown by Leach and Flessas (2003), using the Ermanno-Bernoulli reduction process that the radial reduction variable u1 = J cos y defined the harmonic oscillator of its reduced system of equations. However we observed that this variable may be misleading and had affected the corresponding nonlocal symmetries presented in Leach and Flessas (2003). In this remark, we present the correct radial reduction variable and the corresponding nonlocal symmetries for the system. We also compute nonlocal symmetries of a related dynamical system
·x· + Px + L
gx· = 0 and note that there is a close relationship between these two dynamical systems from their symmetries.
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