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Math Help - Solve For T?

  1. #1
    ain
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    Solve For T?

    Dear all,

    Someone have an idea how to solve my equation below?
    I want to get T1 T2 T3 and T4.

    The main equation:
    T1=u(1)*m1/(cos(theta)*cos(psi))
    T2=u(2)*Ix + Iz*psidot*thetadot - Iy*thetadot*psidot
    T3=[u(3)*Iy - Iz*psidot*phidot + (Jt*Omega + Ix*phidot)psidot]/L
    T4=[u(4)*Iz + Iy*thetadot*phidot - (Jt*Omega + Ix*phidot)thetadot]/L

    To get Omega value, the equation related to T
    Omega = w2 + w4 - w3 - w1
    T1 = b(w1^2 + w2^2 + w3^2 +w4^2)
    T2 = d(-w2^2 - w4^2 + w1^2 +w3^2)
    T3 = b(w1^2 - w3^2)
    T4 = b(w2^2 - w4^2)

    T = [T1 T2 T3 T4]'

    I can solve Omega like below but to get Omega still need T. How should I combine these equation to get T

    % solving of Omega
    omega(1) = 0.0; omega(2) = 0.0; omega(3) = 0.0; omega(4) = 0.0; %initial rotation
    % transformation matrix Q
    Q = [ b b b b;
    d -d d -d;
    b 0 -b 0;
    0 b 0 -b];
    % T = Q * Omega2, where Omega2 = [omega1^2 omega2^2 omega3^2 omega4^2]'
    Omega2 = inv(Q)*T
    %
    for i1 = 1:ni %ni=4
    omega(i1) = sqrt(Omega2(i1));
    end
    % Omega = omega2 + omega4 - oemga1 - omega3
    Omega = omega(2) + omega(4) - omega(1) - omega(3);
    Last edited by CaptainBlack; August 29th 2011 at 07:56 AM.
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  2. #2
    Grand Panjandrum
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    Re: Solve For T?

    Quote Originally Posted by ain View Post
    Dear all,

    Someone have an idea how to solve my equation below?
    I want to get T1 T2 T3 and T4.

    The main equation:
    T1=u(1)*m1/(cos(theta)*cos(psi))
    T2=u(2)*Ix + Iz*psidot*thetadot - Iy*thetadot*psidot
    T3=[u(3)*Iy - Iz*psidot*phidot + (Jt*Omega + Ix*phidot)psidot]/L
    T4=[u(4)*Iz + Iy*thetadot*phidot - (Jt*Omega + Ix*phidot)thetadot]/L

    To get Omega value, the equation related to T
    Omega = w2 + w4 - w3 - w1
    T1 = b(w1^2 + w2^2 + w3^2 +w4^2)
    T2 = d(-w2^2 - w4^2 + w1^2 +w3^2)
    T3 = b(w1^2 - w3^2)
    T4 = b(w2^2 - w4^2)

    T = [T1 T2 T3 T4]'

    I can solve Omega like below but to get Omega still need T. How should I combine these equation to get T

    % solving of Omega
    omega(1) = 0.0; omega(2) = 0.0; omega(3) = 0.0; omega(4) = 0.0; %initial rotation
    % transformation matrix Q
    Q = [ b b b b;
    d -d d -d;
    b 0 -b 0;
    0 b 0 -b];
    % T = Q * Omega2, where Omega2 = [omega1^2 omega2^2 omega3^2 omega4^2]'
    Omega2 = inv(Q)*T
    %
    for i1 = 1:ni %ni=4
    omega(i1) = sqrt(Omega2(i1));
    end
    % Omega = omega2 + omega4 - oemga1 - omega3
    Omega = omega(2) + omega(4) - omega(1) - omega(3);
    That is incomprehensible, try explaining what you are really trying to do, or provide more context please.

    CB
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  3. #3
    A Plied Mathematician
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    Re: Solve For T?

    Quote Originally Posted by CaptainBlack View Post
    That is incomprehensible, try explaining what you are really trying to do, or provide more context please.

    CB
    Agreed. It sounds like you're trying to solve for the vector T = [T1 T2 T3 T4]. However, you appear to have done that already, unless some quantities on the RHS's of your equations, in turn, also depend on the Ti's.
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