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The method of reduction of order and linearization of the two-dimensional Ermakov system

✍ Scribed by A. Maharaj; P. G. L. Leach

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
169 KB
Volume
30
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

We present the general form of the system of second‐order ordinary differential equations invariant under a representation of the Lie algebra sl(2, R) and show that a considerable simplification is achieved using a well‐known Kummer–Liouville transformation. We show that the system can be reduced to a combination of linear second‐order ordinary differential equations and a conservation law. The reduction makes the determination of the complete symmetry group of the standard Ermakov system an easier task than earlier reported (J. Nonlinear Math. Phys. 2005; 12:305–320). The reduced system is equivalent to the reduction of the Kepler problem under a further constraint. Copyright © 2007 John Wiley & Sons, Ltd.

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