Some families of periodic solutions in the planar N-body problem

Details Some families of periodic solutions in the planar N-body problem Some families of periodic solutions in the planar N-body problem

Aug 1976

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976cemec..14....5a&link_type=abstract

(Conference on Mathematical Methods in Celestial Mechanics, 5th, Oberwolfach, West Germany, Aug. 24-30, 1975.) Celestial Mechani

Other

Circular Orbits, Elliptical Orbits, Existence Theorems, Many Body Problem, Orbital Mechanics, Periodic Functions

Scientific paper

The proposition is examined that there exists an infinite number of one-parameter families of symmetric periodic solutions (in rotating coordinate systems), which can be viewed as if one of the mass points of a system of N-1 mass points (N is not less than 3) moving circularly on a straight-line central configuration, is replaced by two mass points moving close to each other in relative elliptical orbits. Existence proofs for these solutions are presented and ways to overcome the inherent degeneracies (resonance) for the periodic motions of circular-elliptical type (only for the case of N = 1), are considered.

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