Lagrangian and near-Lagrangian solutions to the problem of the translational-rotational motion of three rigid bodies

Physics

Scientific paper

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Euler-Lagrange Equation, Rigid Structures, Rotating Bodies, Three Body Problem, Translational Motion, Center Of Gravity, Mass Distribution, Orbital Mechanics

Scientific paper

The author considers the problem of whether there exist exact particular solutions to the general problem of the translational-rotational motion of three rigid bodies possessing three mutually perpendicular symmetry planes, analogous to the Lagrangian solutions to the problem of three point-bodies. Conditions for the existence of such solutions are derived. When the three bodies possess symmetry with respect to an axis and a plane perpendicular to this axis in both external shape and mass distribution, then three types of solutions are admitted which, in Duboshin's terminology (1961), are the types 'three floats', 'three spokes', and 'three shafts', and combinations of these.

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