Relative equilibrium solutions in the four body problem

Details Relative equilibrium solutions in the four body problem Relative equilibrium solutions in the four body problem

Aug 1978

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978cemec..18..165s&link_type=abstract

Celestial Mechanics, vol. 18, Aug. 1978, p. 165-184.

Mathematics

18

Celestial Mechanics, Four Body Problem, Mass Distribution, Motion Stability, Circular Orbits, Equilibrium, Manifolds (Mathematics), Topology, Variational Principles

Scientific paper

Relative equilibrium (RE) solutions in the four-body problem are studied. Consideration is given to the 3 plus 1 problem with three arbitrary finite masses and one infinitesimal mass as well as the general case of four masses represented as the barycentric coordinates of a point of a tetrahedron. Masses for which degeneration occurs are sought along with a division of mass space into regions for which there are different numbers of RE. Two methods are outlined for determining degenerate cases, and manifolds of degeneration are examined together with mass partitions and the corresponding RE. Applications to bifurcation sets of curves are discussed, the linear stability of motion perpendicular to the plane of motion is demonstrated, and the stability of the 3 plus 1 problem is evaluated. It is suggested that both the n-body problem and the case of planets in a narrow belt are linearly stable.

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