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The Rikitake two-disc dynamo system

Published online by Cambridge University Press:  24 October 2008

A. E. Cook  and
P. H. Roberts
A. E. Cook
Affiliation:
Teeside Polytechnic, Middlesbrough.
P. H. Roberts
Affiliation:
Newcastle University School of Mathematics, Newcastle-upon-Tyne.
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Abstract

It is shown that the solution of the Rikitake two-discdynamo system may be described by an orbiting point which, for sufficiently large time, lies arbitrarily close to a limit surface of bounded area. Reversal of the field currents of the dynamo coils are shown to occur in the juxtaposed regions of the two sheets of the limit surface. The two singular points of the system are shown, by Liapounov's direct method, to be unstable foci. An asymptotic theory is developed for the case of small difference in dynamo velocities; the theory is applied to cases of small dissipation in which orbits tend to become nearly periodic with a single oscillation between reversals.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 68 , Issue 2 , September 1970 , pp. 547 - 569
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

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