A manifold of periodic orbits in the planar general three-body problem with equal masses

Details A manifold of periodic orbits in the planar general three-body problem with equal masses A manifold of periodic orbits in the planar general three-body problem with equal masses

Aug 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982a%26a...112..305d&link_type=abstract

Astronomy and Astrophysics, vol. 112, no. 2, Aug. 1982, p. 305-320. Research supported by the Centre National de la Recherche S

Mathematics

14

Manifolds (Mathematics), Mass Distribution, Orbital Mechanics, Three Body Problem, Branching (Mathematics), Collisions, Equations Of Motion, Numerical Stability, Periodic Functions, Symmetry

Scientific paper

The article describes about two dozen families of periodic orbits in the planar general problem of three bodies with three equal masses. These orbits have been obtained with a numerical integration of the regularized equations of motion. The regularization is of the Levi-Civita type and it handles only the three binary collisions. The stability of the periodic solutions is determined on the basis of the two coefficients (a1, a2) of the characteristic equation of the monodromy matrix. A detailed study of the stability coefficients reveals the existence of a large number of critical periodic orbits and bifurcations between different familities. Our study shows several general symmetry properties of the periodic solutions, reminiscent of the restricted problem. It shows seveal important connections of the general problem with some of its special cases: the rectilinear, collinear and isosceles configurations. It finally reveals that several families of periodic solutions terminate with a triple collision orbit.

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