Geometrical unified theory of Rikitake system and KCC-theory

Takahiro Yajima, Hiroyuki Nagahama

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)e203-e210
JournalNonlinear Analysis, Theory, Methods and Applications
Volume71
Issue number12
DOIs
Publication statusPublished - 2009 Dec 15

Keywords

  • Contact tensor calculus
  • Euler-Schouten tensor
  • KCC-theory
  • Nonlinear dynamical systems
  • Rikitake system
  • Unified field theory

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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