Statistics – Computation
Scientific paper
Nov 1975
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975cemec..12..255h&link_type=abstract
Celestial Mechanics, vol. 12, Nov. 1975, p. 255-276.
Statistics
Computation
63
Celestial Mechanics, Motion Stability, Orbit Calculation, Periodic Variations, Three Body Problem, Equations Of Motion, Gravitational Fields, Jacobi Matrix Method, Numerical Integration
Scientific paper
A method is developed to study the stability of periodic motions of the three-body problem in a rotating frame of reference, based on the notion of surface of section. The method is linear and involves the computation of a 4 x 4 variational matrix by integrating numerically the differential equations for time intervals of the order of a period. This linear stability analysis is used to study the stability of a family of periodic motions of three bodies with equal masses, in a rotating frame of reference. This family represents motion such that two bodies revolve around each other and the third body revolves around this binary system in the same direction to a distance which varies along the members of the family. It was found that a large part of the family, corresponding to the case where the distance of the third body from the binary system is larger than the dimensions of the binary system, represents stable motion. The nonlinear effects to the linear stability analysis are studied by computing the intersections of several perturbed orbits with one of the surfaces of section.
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