On the symmetry of solutions in the many-body problem

Details On the symmetry of solutions in the many-body problem On the symmetry of solutions in the many-body problem

Dec 1978

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978sva....22..736l&link_type=abstract

(Astronomicheskii Zhurnal, vol. 55, Nov.-Dec. 1978, p. 1293-1300.) Soviet Astronomy, vol. 22, Nov.-Dec. 1978, p. 736-740. Transl

Astronomy and Astrophysics

Astronomy

Celestial Mechanics, Equations Of Motion, Many Body Problem, Problem Solving, Symmetry, Trajectory Analysis, Three Body Problem, Time Functions

Scientific paper

The possible existence of symmetric solutions to the equations of motion of the N-body problem in an absolute coordinate system is investigated. It is noted that such solutions are known to exist in the restricted three-body problem. Proof is given that symmetric solutions in the N-body problem can exist only if the trajectories of some of the bodies are planar or symmetrical with respect to a plane, line, or point with symmetric laws of motion. Reasons for the existence of the well-known symmetric solutions in the restricted three-body problem are determined.

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