Some aspects of Rikitake system of dynamical equations

• Autorzy: Poria S. , Chakraborty B. K. , Mazumdar H. P.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

dynamical system; stability analysis; integrals of motion; feedback control

PL

dynamika; układ dynamiczny; analiza stabilności; sprzężenie zwrotne

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2003
• Tom: Vol. 8, no 1
• Strony: 87--96
• Opis fizyczny: Bibliogr. 8 poz., wykr.

Twórcy

autor

Poria S.

• Department of Mathematics, Midnapur College Midnapur, West Bengal, INDIA

autor

Chakraborty B. K.

• Sodepur Deshbandhu Vidyapith For Boys Sodepur, 24 Parganas (North), West Bengal, INDIA

autor

Mazumdar H. P.

• Physics and Applied Mathematics Unit Indian Statistical Institute, Calcutta - 700035, INDIA

Bibliografia

• [1] Balachandran K. and Dauer J.P. (1999): Elements of Control Theory. - London: Narosa Publishing House.
• [2] Gupta N. (1992): Integrals of motion for the Lorenz system. - Journal of Mathematical Physics, vol.34, No.2, pp.801-804.
• [3] Kapitaniak T. and Bishop S.R. (1999): The Illustrated Dictionary of Nonlinear Dynamics and Chaos. - New York: John Wiley & Sons.
• [4] Korsch H.J. and Jodl H.J. (1998): Chaos. - New York: Springer Verlag.
• [5] Lorenz E.N. (1963): Deterministic nonperiodic flows.- Journal of the Atmospheric Science, vol.20, pp.130-141.
• [6] Rikitake T. (1958): Oscillations of a system of disk dynamics. - Cambridge Philosophical Society, vol.54, pp.89-105.
• [7] Shahverdiev E.M. (1998): Chaos control in photoconductors. - arXiv.cond-mat/9808045, vol.l, No.5, August.
• [8] Yincent T.L. and Yu J. (1991): Control of chaotic system. - Dynamics and Control, vol.l, pp.35-52.