Abstract
A proof is offered of the existence of periodic solutions of the general problem of three bodies, of the third sort envisaged by Poincaré, that is, arising by analytic continuation from unperturbed keplerian motion of each of two bodies about a primary, in which the two orbits are of commensurable periods, of zero eccentricity, but lying in different planes, provided that the inclination of the two planes is sufficiently small (but not zero).
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Message, P.J. On the existence of periodic solutions of Poincare's third sort in the general problem of three bodies in three dimensions. Celestial Mechanics 28, 107–118 (1982). https://doi.org/10.1007/BF01230663
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DOI: https://doi.org/10.1007/BF01230663