1970/09/01 by A. E. Cook, Andy Cook, Paul Roberts +1
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Geomagnetism and Paleomagnetism Studies #Magnetic and Electromagnetic Effects #Solar and Space Plasma Dynamics
paper · doi:10.1017/s0305004100046338
openalex publication_date 1970/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.