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) .

Read more about this topic:  n-body Problem

Famous quotes containing the words global, solution and/or problem:

    “However global I strove to become in my thinking over the past twenty years, my sons kept me rooted to an utterly pedestrian view, intimately involved with the most inspiring and fractious passages in human development. However unconsciously by now, motherhood informs every thought I have, influencing everything I do. More than any other part of my life, being a mother taught me what it means to be human.”
    —Mary Kay Blakely (20th century)

    “To the questions of the officiously meddling police Falter replied absently and tersely; but, when he finally grew tired of this pestering, he pointed out that, having accidentally solved “the riddle of the universe,” he had yielded to artful exhortation and shared that solution with his inquisitive interlocutor, whereupon the latter had died of astonishment.”
    —Vladimir Nabokov (1899–1977)

    “Every child is an artist. The problem is how to remain an artist once he grows up.”
    —Pablo Picasso (1881–1973)