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Math Help - differential equation

  1. #1
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    differential equation

    Hi!

    The equation:

    -sin(y) + sin(x) = y''

    (of course y=y(x) and y'' means (d^2y)/(dx^2) )


    I'm looking for solution (elliptical integral maybe?), or at least an advice how to solve this.
    The numerical solution (runge kutta or something) with Mathematica or Mathlab will also be very good.
    I just have no idea how to solve this, and if anyone has done something similar, please advice!!!

    Thanks
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  2. #2
    Super Member
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    Well, y=x is an obvious solution, but for a more general one (or less trivial) I really don't know how to attack this. To give you an idea you could try this
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by henry25 View Post
    Hi!

    The equation:

    -sin(y) + sin(x) = y''

    (of course y=y(x) and y'' means (d^2y)/(dx^2) )


    I'm looking for solution (elliptical integral maybe?), or at least an advice how to solve this.
    The numerical solution (runge kutta or something) with Mathematica or Mathlab will also be very good.
    I just have no idea how to solve this, and if anyone has done something similar, please advice!!!

    Thanks
    What is the context (how has this equation arisen)? Looks like an undamped forced pendulum to me.

    Numerical solution (at least for a duration that is not too long) is trivial but will require initial conditions.

    CB
    Last edited by CaptainBlack; December 30th 2009 at 11:33 PM.
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  4. #4
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    Yes, it is compound pendulum.
    The pendulum is forced to fluctuate by momentum, that looks like Asin(t*omega)
    I put x for the time and y for angle.

    So initial conditions can be: y(0)=0 and y'(0)=0.
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