The existence of global solution of the N-body problem

Details The existence of global solution of the N-body problem The existence of global solution of the N-body problem

Jun 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985acasn..26..333w&link_type=abstract

(Acta Astronomica Sinica, vol. 26, no. 4, 1985, p. 333-342) Chinese Astronomy and Astrophysics (ISSN 0275-1062), vol. 10, June 1

Mathematics

Equations Of Motion, Many Body Problem, Transformations (Mathematics), Conformal Mapping, Convergence, Power Series, Singularity (Mathematics)

Scientific paper

By improving the McGehee transformation, a new set of variables is proposed to overcome the difficulties resulting from the singularities, and a method for determining the global solution of the n-body problem is discussed. The transformation makes the time interval of the existence of every largest continued solution correspond to the interval (infinity, + infinity) in the variable tau. Global solutions revert to their original natural meaning, and the size of the time interval of existence is unified before continuing the solution. The process of estimating the analytic region is very simple, though the present results are of limited value for practical calculation because the convergence of the power series is unsatisfactory.

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