The positions of relative equilibrium in the circular orbit of an elastic artificial satellite and their stability

Abstract

The problem of the stability of motion in a circular orbit in a central Newtonian field of force of an elastic artificial satellite, modelled as a free solid body with an arbitrary elastic section connected to it, is considered in a limited formulation. Using Routh's theorem and assuming that the vector of small deformations of the elastic section can be represented in the form of a finite series in the known eigenmodes of its free oscillations [1]and certain others, the positions of relative equilibrium of the spacecraft (numbering 24) are obtained. The positions of equilibrium in which the elastic section is deformed are found approximately. The sufficient conditions for the stability of the positions of equilibrium obtained are found, and the necessary and sufficient conditions that the elastic section should be undeformed in a position of equilibrium are indicated. An example of an artificial satellite modelled as a solid body with an arbitrary rectilinear elastic rod attached to it is considered.