Geometrical unified theory of Rikitake system and KCC-theory |
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Authors: | Takahiro Yajima Hiroyuki Nagahama |
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Institution: | Department of Geoenvironmental Sciences, Graduate School of Science, Tohoku University, Aoba-ku, Sendai 980-8578, Japan |
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Abstract: | The Rikitake system as nonlinear dynamical systems in geomagnetism can be studied based on the KCC-theory and the unified field theory. Especially, the behavior of the magnetic field of the Rikitake system is represented in the electrical system projected from the electro-mechanical unified system. Then, the KCC-invariants for the electrical and mechanical systems can be obtained. The third invariant as the torsion tensor expresses the aperiodic behavior of the magnetic field. Moreover, as a result of the projection, a protrusion between the mechanical and electrical systems is represented by the Euler-Schouten tensor. This Euler-Schouten tensor and the third invariant consist of the same mutual-inductance. Therefore, the aperiodic behavior of the magnetic field can be characterized by the protrusion between the electrical and mechanical systems. |
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Keywords: | 34A26 34A34 37N05 53B40 53B50 70F25 70H03 86A25 |
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