Translational-Rotational Motions of a Rod in the Circular Sitnikov Problem

We study translational-rotational motions of a homogeneous rod of small mass governed by the circular restricted three-body problem for attracting bodies of equal mass. We show that the equations of spatial motions of the rod admit an integral manifold that corresponds to such motions of the rod at which the center of mass of the rod moves along the normal to the plane of rotation of the main bodies and the rod continuously rotates around the normal at the angle equal to π/2.