Families of periodic solutions in problem of solid body rotation at triangular libration point in restricted three-body problem

Physics

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Artificial Satellites, Librational Motion, Three Body Problem, Orbital Mechanics, Periodic Functions, Solids, Triangles

Scientific paper

Satellite rotations at libration points is important due to the development of numerous plans for using libration points of the earth-moon system. By modeling a satellite as a solid body, it is possible to study its rotation around the libration points. Triangular libration points are of the greatest interest because the motion of the center of mass of the solid body at these points is stable. The theory of periodic Poincare solutions was used earlier to study families of periodic solutions for a solid body situated at the triangular libration point of the restricted (circular or elliptical) three-body problem. This article represents a continuation of the aforementioned study and is devoted to periodic regimes of rotational motion of a solid body near the triangular libration point of the restricted three-body problem. A study is also made of new families of periodic solutions. The basis for this research is the theory of periodic Poincare solutions for Hamiltonian systems of the standard type and the equations of rotational motion in normalized canonical variables.

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