Effects of the Earth Magnetic Field and Tidal Force on Oscillations of Cable-Connected Satellites System in Elliptical Orbit

摘要

Combined effects of magnetic field of the earth and tidal forces on the non-linear oscillations of cable-connected satellites system in the central gravitational field of the earth have been studied. The system comprises of two satellites connected by a light flexible and inextensible cable. The satellites are considered to like to be changed material particles, whose centre of mass is moving in elliptical orbit. The central gravitational field of the earth has been taken to be the main force governing the motion. The combined effects of tidal faces and the magnetic field of the earth are considered to be perturbing forces. The dipole of the earth has its axis inclined from the polar axis of the earth by 11.4′. The non-linear oscillation of the system under the combined influence of the earth magnetic field and the tidal forces has been considered about the equilibrium position. This equilibrium position is found to be stable in the sense of Liapunov. In the present paper we have discussed in detail, non-linear oscillations of cable-connected satellites system about the equilibrium position in the neighbourhood of main resonance ω = 1, under the combined influence of the earth magnetic field and the tidal forces; exploiting the method of Bogoiubov, Krilov and Mitropolsky, considering 'e' to be a small parameter the amplitude of oscillations suffers discontinuity in the neighbourhood of main resonance ω = 1. This discontinuity in the amplitude of oscillations occurs at a frequency greater than the resonance frequency.