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Math Help - solving a system of transcendental equations

  1. #1
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    solving a system of transcendental equations

    hi,
    I want to solve the system of three transcendental equations for A, B & C.

    0.97*cos(B)*cos(C)-0.18*cos(B)*sin(C)+ 0.01*sin(B)=0.6304

    0.97*(-cos(A)*sin(C)-sin(A)*sin(B)*cos(C))-0.18*cos(A)*cos(C)+sin(A)*sin(B)*sin(C))-0.01*(sin(A)*cos(B))=0.7235

    0.97*(sin(A)*sin(C)+cos(A)*sin(B)*cos(C)-0.18*-sin(A)*cos(C)+cos(A)*sin(B)*sin(A))-0.01*(cos(A)*cos(B))= -0.2981

    Kindly suggest any analytical or numerical way of solving it. I have already tried the symbolic toolbox in matlab and it gives incomprehensible solutions.
    I also tried eliminating A from equations ----2 and ----3 and solving the resultant two equations. This approach results in 0=0 kind of problem.

    Many thanks for your inputs,
    Yours Truely
    Ganesh
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by ganesh_lg View Post
    hi,
    I want to solve the system of three transcendental equations for A, B & C.

    0.97*cos(B)*cos(C)-0.18*cos(B)*sin(C)+ 0.01*sin(B)=0.6304

    0.97*(-cos(A)*sin(C)-sin(A)*sin(B)*cos(C))-0.18*cos(A)*cos(C)+sin(A)*sin(B)*sin(C))-0.01*(sin(A)*cos(B))=0.7235

    0.97*(sin(A)*sin(C)+cos(A)*sin(B)*cos(C)-0.18*-sin(A)*cos(C)+cos(A)*sin(B)*sin(A))-0.01*(cos(A)*cos(B))= -0.2981

    Kindly suggest any analytical or numerical way of solving it. I have already tried the symbolic toolbox in matlab and it gives incomprehensible solutions.
    I also tried eliminating A from equations ----2 and ----3 and solving the resultant two equations. This approach results in 0=0 kind of problem.

    Many thanks for your inputs,
    Yours Truely
    Ganesh
    This is not the most elegant method of doing this, but is certainly the fastest.

    Rewrite your equations in the form:

    f_1(A,B,C)=0
    f_2(A,B,C)=0
    f_3(A,B,C)=0

    Form the objective function:

     <br />
O(A,B,C) =f_1(A,B,C)^2+f_2(A,B,C)^2+f_3(A,B,C)^2<br />

    Then use the Excel solver to minimise O. One result of this are:

    A\approx3.46,\ B\approx -3.07,\ C\approx 2.08

    However I doubt that if this is an approximation to an exact solution that the exact solution is unique. (to the machine prescission this is a solution and to the same prescission it is not unique).

    An approximate solution with all variables in the range \pm \pi is:

    A\approx 0.092,\ B	\approx -0.370,\ C\approx -0.994


    CB
    Last edited by CaptainBlack; April 17th 2009 at 12:36 AM.
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