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Home  >  Volume 26 (March 2014)

5. On Linearizing dynamical systems in 3-D using the inverse cube law by F.I. Arunaye. Volume26, (March, 2014), pp18 – 21.
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In the symmetry analysis of dynamical systems Ermanno-Bernoulli constants were used to reduce the Kepler problem to systems of oscillators and conservation law in both 2-D and 3-D. In this paper we utilize alternative constants obtained from Hamilton vector of the inverse cube law to reduce it to systems of oscillators and conservation law in 3-D. We compared the effectiveness of both reduction constants through their reduction variables in 3-D and note efficient reduction constant. Further we present a proposition which assert the equivalence of the group realizations of the emanating Lie symmetry groups from these two linearization procedures.  

Keywords:Laplace transforms,  Rieman-Liouville fractional integral, Caputo’s fractional derivative, Mittag-Leffler function, Fractional differential equation, Damping.