Bifurcation points in the planar problem of three bodies

Details Bifurcation points in the planar problem of three bodies Bifurcation points in the planar problem of three bodies

Sep 1977

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977cemec..16...35z&link_type=abstract

Celestial Mechanics, vol. 16, Sept. 1977, p. 35-38.

Mathematics

48

Branching (Mathematics), Celestial Mechanics, Three Body Problem, Angular Momentum, Coplanarity, Manifolds (Mathematics)

Scientific paper

An essential parameter in the planar problem of three bodies is the product of the square of the angular momentum and of the total energy. The role of this parameter, which may be called a bifurcation parameter, in establishing regions of possible motions has been shown by Marchal and Saari (1975) and Zare (1976). There exist critical values of this parameter below which exchange between bodies cannot occur. These critical values may be called bifurcation points. This paper gives an analytical criterion to obtain these bifurcation points for any given masses of the participating bodies.

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