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Math Help - Another second order problem

  1. #1
    ain
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    I still need help to convert another system to that form, but this one has four input (u1 ... u4). m1, m2 and m3 are scalar. The dynamic system is:

    xddot = u1
    yddot = (m1/m2)*tan(psi)*u1
    zddot = (-m1/m3)*tan(theta)*sec(psi)*u1
    phiddot = u2
    thetaddot = u3
    psiddot = u4

    Following Ackbeet's method in my other thread, and got like this pattern:
    y1ddot = v1
    y2ddot= v4
    y3ddot = v3
    y4ddot = v2
    y5ddot = (m1/m2)y2v1
    y6ddot = (-m1/m3)(1/sin(psi)) y2y3v1

    May be the final solution can be simplify to be more close to the new form pattern, because in my calculation still has like sin(psi) in y6ddot. I want to check it with Ackbeet's calculation.

    Thank you very much.
    Last edited by Ackbeet; May 19th 2011 at 07:47 PM.
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  2. #2
    A Plied Mathematician
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    I need to know where you want to end up. I'd recommend letting some of your new LHS variables be equal to trig functions, like in the other thread.
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  3. #3
    ain
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    I want to get the standard pattern like before (chained form)

    y1ddot = v1
    y2ddot = v2
    y3ddot = y2v1
    y4ddot = v3
    y5ddot = y4v1
    y6ddot = v4

    Thank you.

    Quote Originally Posted by Ackbeet View Post
    I need to know where you want to end up. I'd recommend letting some of your new LHS variables be equal to trig functions, like in the other thread.
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