Abstract
The evolution of a systemof equations of motion for two viscoelastic spheres in the gravitational field of a massive point mass is considered. Stationary solutions of this system are found, which correspond to generalizations of the co-linear libration points L1 and L2. In this motion, the centers of mass of the two spheres are located on a single line together with the point mass. The rotational motion of the spheres is synchronized in a 1: 1 resonance with each other and with their translational motion. The instability of the stationary solutions obtained is demonstrated.
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