The stability of the stationary motions of a dynamically symmetric solid at a triangular libration point

The motion of a dynamically asymmetric solid relative to its center of mass is investigated in the context of a circular bounded problem for three bodies, with the solid located at a triangular libration point. It is assumed that the motion of the principal bodies M1 and M2 with finite masses of m1 and m2 and the motion of the center of mass of the solid are described by the equations for the plane circular bounded problem of three bodies. The dimensions of the solid are assumed to be small in comparison with the distances from its center of mass to M1 and M2, which makes it possible to disregard the effect of the motion of the solid around its center of mass on the motion of the center of mass proper. The necessary and sufficient conditions for the stability of solutions are determined.