On the existence of periodic solutions of Poincare's third sort in the general problem of three bodies in three dimensions

Details On the existence of periodic solutions of Poincare's third sort in the general problem of three bodies in three dimensions On the existence of periodic solutions of Poincare's third sort in the general problem of three bodies in three dimensions

Oct 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982cemec..28..107m&link_type=abstract

(Conference on Mathematical Methods in Celestial Mechanics, 7th, Oberwolfach, West Germany, Aug. 24-28, 1981.) Celestial Mechani

Mathematics

4

Existence Theorems, Orbital Mechanics, Poincare Problem, Three Body Problem, Eccentricity, Kepler Laws

Scientific paper

A proof is presented for the existence of Poincare's (1892) third kind of periodic solution for the general three-body problem. Such solutions arise through analytic continuation from unperturbed Keplerian motion of each of two bodies about a primary, where the two orbits are of commensurate periods and zero eccentricity, but lie in different planes when their inclination is sufficiently small but greater than zero.

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