Mathieu Equation

Discussion in 'Boat Design' started by netjaws, Dec 1, 2005.

  1. netjaws
    Joined: Jan 2004
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    netjaws Junior Member

    Trying to investigate parametric roll, and don't actually need to SOLVE the Mathieu equation - just need to know whether the solution will be bounded or unbounded.

    Any helps?


    Joshua N Straume
     
    netjaws, Dec 1, 2005
    #1
  2. Guillermo
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    Guillermo Ingeniero Naval

    Guillermo, Dec 1, 2005
    #2
  3. netjaws
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    netjaws Junior Member

    p and q?

    Interestingly, that first article is what posed my question!

    That is - how do we find whether the solution is bounded or unbounded, without actuallly solving it?
     
    netjaws, Dec 2, 2005
    #3
  4. Guillermo
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    Guillermo Ingeniero Naval

    Good question. I don't know.
     
    Guillermo, Dec 2, 2005
    #4

  6. tspeer
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    tspeer Senior Member

    I think Guillermo has put you on the right road - the Christian paper says the imaginary part of the solution's exponent has to be zero for a bounded solution, and the boundary curves shown on the Ince-Strutt diagram _are_ the conditions that separate the bounded from the unbounded solutions.

    You might try looking for a Lyapunov function for the problem and finding the bounds on that. Zounes and Rand use the function L(phi) = p*phi and present a number of ways of finding the stability contours. Zhang and Li use the same Lyapunov function, too, so I suspect it's the way to go.

    It looks like a really hairy problem!
     
    tspeer, Dec 3, 2005
    #5
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