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:
- 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.
- 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 
.
Read more about this topic: n-body Problem
Famous quotes containing the words global, solution and/or problem:
“Ours is a brand—new world of allatonceness. “Time” has ceased, “space” has vanished. We now live in a global village ... a simultaneous happening.”
—Marshall McLuhan (1911–1980)
“Coming out, all the way out, is offered more and more as the political solution to our oppression. The argument goes that, if people could see just how many of us there are, some in very important places, the negative stereotype would vanish overnight. ...It is far more realistic to suppose that, if the tenth of the population that is gay became visible tomorrow, the panic of the majority of people would inspire repressive legislation of a sort that would shock even the pessimists among us.”
—Jane Rule (b. 1931)
“My problem lies in reconciling my gross habits with my net income.”
—Errol Flynn (1909–1959)