TY - JOUR
T1 - Geometrical unified theory of Rikitake system and KCC-theory
AU - Yajima, Takahiro
AU - Nagahama, Hiroyuki
N1 - Funding Information:
One of the authors (TY) was financially supported by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists and is now supported by the Global COE (Centers of Excellence) Program: “Global Education and Research Center for Earth and Planetary Dynamics” of Tohoku University.
Copyright:
Copyright 2010 Elsevier B.V., All rights reserved.
PY - 2009/12/15
Y1 - 2009/12/15
N2 - 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.
AB - 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.
KW - Contact tensor calculus
KW - Euler-Schouten tensor
KW - KCC-theory
KW - Nonlinear dynamical systems
KW - Rikitake system
KW - Unified field theory
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U2 - 10.1016/j.na.2008.10.017
DO - 10.1016/j.na.2008.10.017
M3 - Article
AN - SCOPUS:72149127670
VL - 71
SP - e203-e210
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
SN - 0362-546X
IS - 12
ER -