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1 International Journal of Applied Mechanics and Engineering

1 2003

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Some aspects of Rikitake system of dynamical equations

Poria S., Chakraborty B. K., Mazumdar H. P.

International Journal of Applied Mechanics and Engineering

2003

Vol. 8, no 1

87-96

In this paper, some characteristic features of a dynamical system proposed by Rikitake (1958), as a model for the self-generation of the Earth's magnetic field by large current carrying eddies in the core are examined. First, a linear stability analysis of a fixed point of the Rikitake system of three dynamical equations is made. Next, utilizing the conjecture that an integral of motion must assume constant value when evaluated at a singularity, a few integrals of motion of the Rikitake system are worked out. Finally, the effects of a linear feedback control on the linearized versions of the Rikitake system in terms of state perturbation variables, are investigated. The dynamical equations are solved numerically by the fourth order Runge-Kutta method. The results are presented graphically and discussed.