Celestial Mechanics and Dynamical Astronomy

, Volume 50, Issue 1, pp 73-88

The global solution of the N-body problem

  • Wang Qiu-DongAffiliated withDepartment of Mathematical Science, University of Cincinnati

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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.

Key words

N-body problem blowing up transformation analytic continuation