The global solution of the N-body problem

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

Mar 1990

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990cemda..50...73w&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, Volume 50, Issue 1, pp.73-88

Astronomy and Astrophysics

Astronomy

1

Scientific paper

The problem of finding a global solution for systems in celestial mechanics was proposed by Weierstrass during the last century. More precisely, the goal is to find a solution of the n-body problem in series expansion which is valid for all time. Sundman solved this problem for the case of n = 3 with non-zero angular momentum a long time ago. Unfortunately, it is impossible to directly generalize this beautiful theory to the case of n > 3 or to n = 3 with zero-angular momentum. A new ‘blowing up’ transformation, which is a modification of McGehee's transformation, is introduced in this paper. By means of this transformation, a complete answer is given for the global solution problem in the case of n > 3 and n = 3 with zero angular momentum.

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