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Math Help - Catenary equation given 2/3 points

  1. #1
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    Question Catenary equation given 2/3 points

    Hi there!

    I'm working on a research about catenaries and its use related to architectural and structural problems, something sort of interesting. And I just came across a really unexpected problem.

    The thing is that I'm including some pics on catenaries (Gaudi, St Paul's Cathedral, St Louis Gateway arch...) and it would be great to draw their catenaries on the pics and describe their equations. The thing is catenary equation is (I'm working on arches, so that's why the minus sign; and they are simmetrical, nothing-weird curves):

    y(x) = b - a*cosh(x/a)

    (okay there should be one more argument, y(x) = b - a*cosh(x/a+c))

    How do you get software like Maple / Derive solve such a system of equations? I have pics, so I can make up any x-y value correlation, but they simply come up with unsatifactory answers (undefine, floating point)... I guess I'm looking for an approximation or something. Don't really know, I have never worked with these stuff before. Really, any help would be greatly appreciated, really! this is driving me insane, and it must be easy.
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  2. #2
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    Perhaps I'm confused as usual, but I don't see a "system" of equations to solve. Will this be of any help?...

    Catenary - Wikipedia, the free encyclopedia
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  3. #3
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    Yes, sorry, I was too focused on the issue and thought it was evident.
    Mmm... I've got pics of catenaries, so there's no problem to obtain x and y values. For example:

    http://3.bp.blogspot.com/_obrjUraoDH...ry-arch_2m.jpg

    So, let's say the people on the picture are 1.7m tall. That gives us (considering catenary simetrical around y-axis and ground level as x-axis):
    x=0 --> y=1.7
    x=-1.2 --> y=0
    x=+1.2 --> y=0 (because of the simetry)

    So we get a set of two equations:
    1.7=b-a*cosh(0)
    0=b-a*cosh(1.2/a)

    which is not easy to solve by hand (perhaps by using approximations... ZzZz...) and computer programs seem to be unable to calculate a solution either. That's the problem. How would you get Maple or Derive or another program solve such system of equations?
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