IJPAM: Volume 78, No. 6 (2012)

SOME NON-LINEAR RESONANCE OSCILLATIONS OF
DUMBELL SATELLITE IN ELLIPTICAL ORBIT

A. Narayan$^1$, M.D. Pandey$^2$, Amitesh Narayan$^3$
$^{1,2,3}$Department of Mathematics
Bhilai Institute of Technology
Bhilai House Durg
Pilani Rajasthan, INDIA


Abstract. Some non-linear oscillations of Dumbell satellite in elliptical orbit in the central gravitational field of force under the combined influence of Earth magnetic field, oblateness of the Earth and some external periodic forces of general in nature has been studied. The system comprises of two charged material particles connected by a light flexible and inextensible cable, moves with taut cable like a dumbbell satellite, in elliptical orbit around the Earth. The central gravitational field of force is the main force governing the motion and various perturbing forces influencing the system are disturbing in nature. Non-linear oscillations of dumbbell satellite about the equilibrium position in the neighbourhood of the main resonance $\omega$=1, has been studied, exploiting the asymptotic method due to Bogoliubov, Krilov and Metropolosky, considering `e'to be a small parameter. The analysis of stability of the system has been discussed due to Poincare method.

Received: March 16, 2012

AMS Subject Classification: 70F15

Key Words and Phrases: non-linear oscillations, dynamical system, perturbing forces, cable connected satellite

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 78
Issue: 6