Dynamics of gravitational system "satellite-stabilizer"

with maximal speed of response

V.A.Sarychev

Keldysh Institute of Applied Mathematics, Moscow, Russia

Universidade da Beira Interior, Covilhã, Portugal.

A.M.Seabra

Escola Superior de Tecnologia de Viseu, Viseu, Portugal

 

Dynamics of a satellite-stabilizer system is studied. The stabilizer is a mass at the end of a boom which is linked to the centre of mass of the satellite through a dissipative hinge mechanism. Centring springs fix the position of the stabilizer to the satellite. The paper discusses small oscillations of the system in the plane of a circular orbit in vicinity of equilibria. The axis angles , љcharacterize respectively the attitude of the satellite and the stabilizer relative to the tangent to the circular orbit. The necessary and sufficient conditions of asymptotic stability of the equilibrium positions were examined using Lienard and Chipart criterion. The main propose of the work is to obtain optimal parameters which provide minimum duration of the damping of the system. Here it is done using the concept of degree of stability δ which is represented as the absolute value of the real part of the root of the characteristic polynomial which is closest to the imaginary axis. Maximizing δ optimal parameters and equilibria are obtained. It is shown that for all equilibrium positions the satellite is a plane, the boom is normal to that plane and maximum degree of stability .