On the Manifold "Gravitational Propeller" in the Generalized Circular Sitnikov Problem

The orbit-attitude behaviors of a homogeneous rod of small mass in the circular restricted three-body problem with primaries of equal mass are investigated. A new type of motion is described for the rod whereby its barycenter moves along the normal to the plane of rotation of the two primaries, whilst the rod itself rotates continuously around the normal, forming a constant angle of pi/2 with it (the manifold "gravitational propeller"). It is also shown that this manifold includes, as a special case, two types of motions of the rod. The first type is rotations with a constant angular velocity, which coincides with the angular velocity of the primaries. The second type is uneven rotations in the plane of motion of the two primaries. A manifold of motions also exists, where the rod moves translationally along the normal, being directed along it. A description of motions is presented for these manifolds.