Resonance in Satelliteâ€™s Motion Under Air Drag

Mani Sethi,Rashmi Bhardwaj

doi:10.3844/ajassp.2006.2184.2189

Abstract

This article studies the attitude motion of a satellite in a circular orbit under the influence of central body of mass M and its moon of mass m, whose orbit is assumed to be circular and coplanar with the orbit of the satellite. The body is assumed to be tri-axial body with principal moments of inertia A < B < C at its centre of mass, C is the moment of inertia about the spin axis which is perpendicular to the orbital plane. These principal axes are taken as the co-ordinate axes x, y, z; the z axis being perpendicular to the orbital plane. We have studied the rotational motion of satellite in the circular orbit under the influence of aerodynamic torque. Using BKM method, it is observed that the amplitude of the oscillation remains constant upto the second order of approximation. The main and the parametric resonance have been shown to exist and have been studied by BKM method. The analysis regarding the stability of the stationary planar oscillation of a satellite near the resonance frequency shows that the discontinuity occurs in the amplitude of the oscillation at a frequency of the external periodic force which is less than the frequency of the natural oscillation.

Highlights

The determination and prediction of the orbit of a satellite in the near-earth environment is complicated by the fact that the satellite is influenced by the dissipative effects of the earth’s atmosphere
None of them have studied the effect of aerodynamic torque on the attitude motion of a satellite in circular orbit
From the equations (8) & (10), we observe that the amplitude of the oscillation remains constant even upto the second order of approximation of the aerodynamic torque parameter ε and the equation (7) gives us the main resonance at ω = ±1 and the parametric resonance at ω = ± 1, k ∈I . 2k +1

Summary

INTRODUCTION

The determination and prediction of the orbit of a satellite in the near-earth environment is complicated by the fact that the satellite is influenced by the dissipative effects of the earth’s atmosphere. FerrazMello, Michtchenko[5], discussed the Dynamics of Two Planets in the 3/2 Mean-motion Resonance in Application to the Planetary System of the Pulsar PSR B1257+12. Beaugé et al.[6,7] studied Planetary migration and extra solar planets in the 2/1 meanmotion resonance They reviewed recent results on the dynamics of multiple-planet extra-solar systems, including main sequence stars and the pulsar PSR B1257+12 and comparatively, our own Solar System. They discussed Resonances and stability of extra-solar planetary systems. Euler’s equation of motion about z-axis, taking v (true anomaly as an independent variable) is obtained as:. Where the amplitude a and the phase ψ are determined by differential equations da dv ε A1 (a )

In our problem

CONCLUSION