The influence of inertia and gravity forces on deformation of an elastic beam clamped in the body of an orbital gyrostat

In the restricted formulation, we consider the motion of a gyrostat with an elastic beam clamped in its body by one end along a Keplerian circular orbit in a Newtonian central force field. The rectilinear axis of the undeformed beam is placed into the symmetry plane of the principal central ellipsoid of intertia of the mechanical system. The inextensible beam is subjected to infinitesimal space deformations in the process of the motion of the system. Under certain assumptions, in the semi-inverse statement we study the special relative equilibria (the states of rest of the system except for a rotor in the orbital coordinate system). In the equilibria, the deformed axis of the beam lies either in the plane perpendicular to the local vertical line, or in the orbital plane, or in the plane perpendicular to orbit. The choice for studying such special equilibria is determined by the purpose of the simplest separation of the influence of the inertia and gravitation on the deformation of the beam.