Numerical explorations of the rectilinear problem of three bodies

Details Numerical explorations of the rectilinear problem of three bodies Numerical explorations of the rectilinear problem of three bodies

Jan 1980

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980cemec..21...73b&link_type=abstract

(Conference on Mathematical Methods in Celestial Mechanics, 6th, Oberwolfach, West Germany, Aug. 14-19, 1978.) Celestial Mechani

Computer Science

Numerical Analysis

7

Collisions, Equations Of Motion, Numerical Analysis, Periodic Functions, Three Body Problem, Celestial Mechanics, Coordinates, Graphs (Charts), Independent Variables, Singularity (Mathematics)

Scientific paper

Some results of a numerical exploration of the rectilinear problem of three bodies, with the two outer masses equal, are presented. The equations of motion are first given in relative coordinates and in regularized variables, removing both binary collision singularities in a single coordinate transformation. Among most important results are seven periodic solutions and three symmetric triple collision solutions. Two of these periodic solutions have been continued into families, the outer mass m3 being the family parameter. One of these families exists for all masses while the second family is a branch of the first at a second-kind critical orbit. This last family ends in a triple collision orbit.

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