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:
“The Sage of Toronto ... spent several decades marveling at the numerous freedoms created by a “global village” instantly and effortlessly accessible to all. Villages, unlike towns, have always been ruled by conformism, isolation, petty surveillance, boredom and repetitive malicious gossip about the same families. Which is a precise enough description of the global spectacle’s present vulgarity.”
—Guy Debord (b. 1931)
“Let us begin to understand the argument.
There is a solution to everything: Science.”
—Allen Tate (1899–1979)
“The great problem of American life [is] the riddle of authority: the difficulty of finding a way, within a liberal and individualistic social order, of living in harmonious and consecrated submission to something larger than oneself.... A yearning for self-transcendence and submission to authority [is] as deeply rooted as the lure of individual liberation.”
—Wilfred M. McClay, educator, author. The Masterless: Self and Society in Modern America, p. 4, University of North Carolina Press (1994)