Newsgroups: comp.arch Path: utzoo!henry From: henry@utzoo.uucp (Henry Spencer) Subject: Re: Seeing the future Message-ID: <1988Nov28.195846.921@utzoo.uucp> Organization: U of Toronto Zoology References: <1984@eos.UUCP> <28200245@mcdurb>Date: Mon, 28 Nov 88 19:58:46 GMT In article jeff@lorrie.atmos.washington.edu (Jeff L. Bowden) writes: > >What is the n-body problem? Given n objects in space, considering each as a point mass affected by no forces other than gravity (for simplicity's sake), predict their positions and velocities in the future given initial positions and velocities. For n=1, it's trivial. Newton solved n=2. Doing n=3 algebraically is incredibly hard, and common wisdom hath it that it is impossible. Not true; there is a little-known but valid solution using somewhat exotic infinite series. (It *is* provably unsolvable using "finite" mathematics.) Unfortunately the infinite-series solution is of no practical use: it converges too slowly. There are useful algebraic solutions for some very restricted special cases of n=3. For practical n=3 work, and any work for n>3, one must use iterative numerical approximations. Making them efficient for large n is hard. Hence the interest in the new approach. -- Sendmail is a bug, | Henry Spencer at U of Toronto Zoology not a feature. | uunet!attcan!utzoo!henry henry@zoo.toronto.edu