Geometrical unified theory of Rikitake system and KCC-theory

Takahiro Yajima, Hiroyuki Nagahama

Research output: Contribution to journalArticle

12 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
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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