Particular solutions to the problem of three bodies possessing two mutually perpendicular planes of symmetry

Astronomy and Astrophysics – Astronomy

Scientific paper

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Astronomical Coordinates, Equations Of Motion, Gravitational Effects, Three Body Problem, Axes Of Rotation, Center Of Mass, Symmetry

Scientific paper

The conditions governing the existence of collinear motions of the mass centers of three bodies are obtained using a strict expression for the force function in multiple integral form. It is assumed that each of these bodies is dynamically symmetrical with respect to two mutually perpendicular planes. These motions are accompanied by the rotation of bodies around the axes perpendicular to the plane of motion of mass centers.

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