Stability of Relative Equilibrium of a Spacecraft Composed of the Two Rigid Bodies Linked with the Elastic Rod

The problem is considered for stability of a relative equilibrium of a mechanical system in orbit that consists of two solid bodies connected by a thin inextensible elastic rod. The problem for stability of a relative equilibrium position reduces to the problem of a minimum of a changed potential system energy comprising the potential energy of elastic, gravitational and centrifugal forces.