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)

    “Who shall forbid a wise skepticism, seeing that there is no practical question on which any thing more than an approximate solution can be had? Is not marriage an open question, when it is alleged, from the beginning of the world, that such as are in the institution wish to get out, and such as are out wish to get in?”
    —Ralph Waldo Emerson (1803–1882)

    “What had really caused the women’s movement was the additional years of human life. At the turn of the century women’s life expectancy was forty-six; now it was nearly eighty. Our groping sense that we couldn’t live all those years in terms of motherhood alone was “the problem that had no name.” Realizing that it was not some freakish personal fault but our common problem as women had enabled us to take the first steps to change our lives.”
    —Betty Friedan (20th century)