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:

    Much of what Mr. Wallace calls his global thinking is, no matter how you slice it, still “globaloney.” Mr. Wallace’s warp of sense and his woof of nonsense is very tricky cloth out of which to cut the pattern of a post-war world.
    Clare Boothe Luce (1903–1987)

    Give a scientist a problem and he will probably provide a solution; historians and sociologists, by contrast, can offer only opinions. Ask a dozen chemists the composition of an organic compound such as methane, and within a short time all twelve will have come up with the same solution of CH4. Ask, however, a dozen economists or sociologists to provide policies to reduce unemployment or the level of crime and twelve widely differing opinions are likely to be offered.
    Derek Gjertsen, British scientist, author. Science and Philosophy: Past and Present, ch. 3, Penguin (1989)

    The problem for the King is just how strict
    The lack of liberty, the squeeze of the law
    And discipline should be in school and state....
    Robert Frost (1874–1963)