The topology of manifold M8 of the general three-body problem

Details The topology of manifold M8 of the general three-body problem The topology of manifold M8 of the general three-body problem

Jun 1978

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978acasn..19....1c&link_type=abstract

Acta Astronomica Sinica, vol. 19, June 1978, p. 1-17. In Chinese, with abstract in English.

Mathematics

1

Euler-Lagrange Equation, Manifolds (Mathematics), Three Body Problem, Topology, Angular Momentum, Celestial Mechanics, Coordinate Transformations, Orbital Mechanics, Triangulation

Scientific paper

A more elementary and intuitive method than that used by Smale (1970) and Easton (1975) is applied in a study of the topology of the manifold M8 of the general three-body problem. It is verified that the topology of M8 can vary only when the energy constant passes through the admissible values of Lagrange's particular solutions. The topologies of M8 are indicated for five ranges of energy constant values. Dong's (1974) result concerning the connectedness of M8 is verified by a rigorous proof.

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