Abstract
Parametric resonance driven oscillations of a dumbbell satellite in elliptical orbit in central gravitational field of force under the combined effects of perturbing forces Earth Magnetic field and Oblateness of the Earth has been studied. The system comprises of two satellite connected by a light, flexible and inextensible cable, moves like a dumbbell satellite in elliptical orbit, in central gravitational field of force. The gravitational field of the Earth is the main force governing the motion and magnetic field of the Earth and Oblateness of the Earth are considered to be perturbing forces, disturbing in nature. Non-linear oscillations of dumbbell satellite about the equilibrium position in the neighborhood of parametric resonance \(w=1/2\), under the influence of perturbing forces, which is suitable for exploiting the asymptotic methods of Bogoliubov, Krilov and Metropoloskey has been studied, considering ‘e’ to be a small parameter. The Hamiltonian has been constructed for the problem and phase analysis has been applied to investigate the stability of the system.
Highlights
The system comprises of two satellite connected by a light, flexible and inextensible cable, moves like a dumbbell satellite in elliptical orbit, in central gravitational field of force
This paper is devoted to the analysis of non-linear parametric resonance driven oscillations of cable connected satellites system in elliptical orbit connected by a light, flexible and inextensible cable moving in the central gravitational field of the Earth under the combined effects of the Earth magnetic field and Oblateness of the Earth
Krupa et al 2000 & 2006), (Beletsky & Levin 1993), (Mishra & Modi 1982). All these authors have mentioned numerous important applications of system and stability of relative equilibrium, if the system moves in a circular and elliptical orbit. (Beletsky & Novikova 1969), studied the motion of a system of two satellite connected by a light, flexible and inextensible string in the central gravitational field of force relative to their centre of mass, which is itself assumed to more along a Keplerian elliptical orbit under the assumption that the two satellite are moving in the plane of the centre of mass
Summary
This paper is devoted to the analysis of non-linear parametric resonance driven oscillations of cable connected satellites system in elliptical orbit connected by a light, flexible and inextensible cable moving in the central gravitational field of the Earth under the combined effects of the Earth magnetic field and Oblateness of the Earth. Krupa et al 2000 & 2006), (Beletsky & Levin 1993), (Mishra & Modi 1982) All these authors have mentioned numerous important applications of system and stability of relative equilibrium, if the system moves in a circular and elliptical orbit. (Beletsky & Novikova 1969), studied the motion of a system of two satellite connected by a light, flexible and inextensible string in the central gravitational field of force relative to their centre of mass, which is itself assumed to more along a Keplerian elliptical orbit under the assumption that the two satellite are moving in the plane of the centre of mass. The present paper deals with the non-linear parametric driven oscillation of dumbbell satellite in elliptical orbit under the combined effects of magnetic field of the Earth and oblateness of the. The perturbing force is arising due to magnetic moments, eddy current and hysteresis, out of these the space craft magnetic moment is usually the dominant source of disturbing effects
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