Stability of Extensible Cable Connected Satellite System under Environmental Perturbation Forces in Elliptical Orbit

摘要

The effect of environmental perturbation forces of the earth on the motion and stability of two cable-connected satellites in the earth's central gravitational field of force in elliptical orbit has been studied. In this paper the perturbation forces are the solar radiation pressure, the magnetic field of the Earth and the atmospheric resistance. The cable connecting the two satellites is assumed to be a light, flexible, non-conducting and extensible in nature. The effects of the Earth shadow have been considered during the analysis. The equations of motion of the system have been deduced with respect to the centre of mass, which is assumed to move along a Keplerian elliptical orbit. Hence a set of non-linear, non-homogeneous and non-autonomous differential equations in a rotating frame of reference in Nechvile's coordinates has been obtained for the motion of the system.rnThe Jacobi integral exists for the problem and with the help of this integral, we have discussed analytical and numerical stability of the system, we have used Liapunov sufficient condition for the stability of the system in elliptical orbit.