Geometrical unified theory of Rikitake system and KCC-theory

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.