A. Narayan, M.D. Pandey
Department of Mathematics
Bhilai Institute of Technology
Bhilai House, Durg, India

Abstract. Condition of Non-linear stability of dumbell satellites, in elliptical orbit in the central gravitational field of force under the combined effects of various perturbing forces has been studied. The system comprises of two satellites connected by a light, flexible and inextensible cable, moves with tight cable like a dumbell satellite in elliptical orbit, in the central gravitational field of force. The gravitational field of the Earth is the main force governing the motion and various perturbing forces like magnetic field of the Earth, oblateness of the Earth and forces of general nature are considered to be perturbing forces, disturbing in nature. Non-linear oscillations of dumbell satellites about the equilibrium position in the neighbourhood of main resonance , under the influence of perturbing forces which is suitable for exploiting the method of Bogoliubov-Krilov and Mitropoloskey, has been discussed, considering 'e' to be samll parameter and the condition of stability of dumbell satellites has been discussed using poicare method. It has been observed that the discontinuing in the amplitude of oscillations occur at a frequency less than the natural frequency.This discontinuity of amplitude of oscillations of the system is important for analysing the condition of stability of dumbell satellite in elliptical orbit.

Received: July 6, 2011

AMS Subject Classification: 70F15

Key Words and Phrases: condition of stability, perturbing forces, dynamical system, non-linear oscillation

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