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Math Help - Mass points in equilibrium

  1. #16
    Grand Panjandrum
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    Quote Originally Posted by bobbyk View Post
    But it is! Why don't you try to find the solution instead of saying it's
    impossible?

    Bob
    You tell me at one point that it is a solution, if that is the type of solution
    you had in mind I have found it. But it is not a solution to the question you
    asked.

    RonL
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  2. #17
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by bobbyk View Post
    This was NOT a proposed constructoin, but a trivial example of how an infinite number of masses can add up to 1. If you're not aware of this,
    then we have nothing more to say! You are kidding aren't you?
    Please say you are!
    Bob
    (sigh) Of course I am aware that \sum_{n = 1}^{\infty} \left ( \frac{1}{2} \right ) ^n = 1. The point is that if any of the masses are non-zero then they will be attracted to the rest of the collection and start accelerating. Thus the situation is not static.

    Quote Originally Posted by bobbyk View Post
    But it is! Why don't you try to find the solution instead of saying it's
    impossible?

    Bob
    Perhaps because we can't think of a way to do it?

    I have grave doubts about the possibility of this problem having a solution as stated. I have (vaguely) heard of Ulam, but have never studied any of his books so I can't say for sure, but certainly within the limits of my knowledge of Physics and my creativity I can't think of a way to construct such a series of non-zero masses.

    Until someone can post a workable solution I'm going to have to say that I think it is impossible.

    Perhaps you could try posting your question here. If they do manage to come up with a solution I'd be interested in hearing about it.

    -Dan
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  3. #18
    Forum Admin topsquark's Avatar
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    I suppose there is a possibility. I thought of it more in terms of an electrodynamics problem, rather than gravity.

    If we had, say two point masses (m = 1/2 each), one positioned at + infinity and one at - infinity. This would do the trick. We can, in fact, place any single mass at the origin (or any other point in between.)

    I must add that this isn't really a constructable problem, but as we are already considering point masses at infinity...

    -Dan

    Edit: No, this isn't going to work either, because the masses need to be constrained to [0, 1] on some line, not out at infinity. Ah well.
    Last edited by topsquark; July 28th 2007 at 06:37 AM. Reason: Nope, not this either.
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  4. #19
    Grand Panjandrum
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    Quote Originally Posted by topsquark View Post
    I have (vaguely) heard of Ulam, but have never studied any of his books
    Heresy, Stan Ulam inventor of the Monte-Carlo method and real father of the
    H-bomb, amoung other things.

    RonL
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  5. #20
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by CaptainBlack View Post
    Heresy, Stan Ulam inventor of the Monte-Carlo method and real father of the
    H-bomb, amoung other things.

    RonL
    I knew about neither. As for Monte-Carlo I've always viewed that method with a bit of suspicion. Not that I think it doesn't work (though I've heard of solutions that it's missed) but because you pretty much have to know what the solution is going to be before you start in order for it to work well. (I could be wrong about this; I've never studied how to do it, just quickly read an article about its use once.)

    -Dan
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  6. #21
    Grand Panjandrum
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    Quote Originally Posted by topsquark View Post
    I knew about neither. As for Monte-Carlo I've always viewed that method with a bit of suspicion. Not that I think it doesn't work (though I've heard of solutions that it's missed) but because you pretty much have to know what the solution is going to be before you start in order for it to work well. (I could be wrong about this; I've never studied how to do it, just quickly read an article about its use once.)

    -Dan
    It is essentially a method for doing very high dimensional integrals, as such
    it is just a question of how much precision you want rather than a question
    of it working or not working (at least that is if you can specify the sample
    space and distributions).

    It is essentially a method of last resort, and as we know these occur almost
    all the time in scientific work.

    RonL
    Last edited by CaptainBlack; August 1st 2007 at 10:48 AM.
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  7. #22
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by CaptainBlack View Post
    It is essentially a method of last resort, and as we know these occur almost
    all the time in scientific work.

    RonL
    (snort) Tell me about it! Don't let TPH know, though. It may make him feel that Science isn't exact.

    -Dan
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