Lyapunov Stability Of Tethered Dumbbell Satellites In Elliptical Orbit

Abstract

This paper represents the equilibrium positions and stability of two artificial satellites connected by light, flexible, and elastic long tethers under the combined effect of several classical perturbative forces in an elliptical orbit. The tether may be conducting or non-conducting. In our problem, it is taken as non-conducting in nature. We have treated the problem by taking five perturbative forces on the system simultaneously. Three perturbations exist due to the influences of the earth, namely geomagnetic fields, shadows, and oblateness. The other perturbations are due to the elasticity of the cable and solar light pressure. The effect of air resistance is neglected, considering the satellites as high-altitude satellites. To determine the stability of the satellites, we have used the Lyapunov method. The dynamical behaviors of the satellites are represented by differential equations. Based on analytical analysis of the differential equations of motion, we get the equilibrium positions of the system concerned in elliptical orbit. Lyapunov method gives the equilibrium position as unstable as expected.