The problem of three rigid bodies

Physics

Scientific paper

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Celestial Mechanics, Rotating Bodies, Three Body Problem, Translational Motion, Equations Of Motion, Equatorial Orbits, Euler-Lagrange Equation

Scientific paper

The translational-rotational motion of three rigid bodies is investigated analytically. It is shown that particular solutions analogous to the Lagrangian and Eulerian solutions of the classical problem exist under certain specified conditions: if each body has axial symmetry with respect to the equatorial plane, there are solutions in which the centers of mass form an equilateral triangle or lie on a straight line, and each body maintains a constant orientation relative to the plane of motion of the mass centers. An interaction law for each pair of bodies is derived.

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