n-body Problem - The Global Solution of The n-body Problem

The Global Solution of The n-body Problem

In order to generalize Sundman's result for the case n > 3 (or n = 3 and c = 0) one has to face two obstacles:

  1. As it has been shown by Siegel, collisions which involve more than 2 bodies cannot be regularized analytically, hence Sundman's regularization cannot be generalized.
  2. The structure of singularities is more complicated in this case: other types of singularities may occur.

Finally Sundman's result was generalized to the case of n > 3 bodies by Q. Wang in the 1990s. Since the structure of singularities is more complicated, Wang had to leave out completely the questions of singularities. The central point of his approach is to transform, in an appropriate manner, the equations to a new system, such that the interval of existence for the solutions of this new system is [0,\infty) .

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