Periodic rotations of a rigid body located at the libration point

Abstract

Periodic rotations of a rigid body close to the flat motions were found. Their orbital stability was investigated. Analysis was done up to second order of the small parameter. It was proved that solutions found are orbitally stable except of the third order resonance case. This resonance do not appear if terms up to the first order of small parameter are considered only.

Periodic Motion of Rigid Body in Circular Orbit

“…Assuming that polar and equatorial moments of inertia are almost equal and projection of the angular velocity onto symmetry axis is small, Markeev [3] proved the existence of spatial periodic solutions close to the flat ones. Maciejewski and Níedzíelska [5] adopted the method of Markeev to solve a similar problem for a rigid body whose mass center is located at the triangular libration point of the restricted three-body problem. They found that some results of Markeev [3] are incorrect and they presented a new, revised analysis.…”