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);

Quote:

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Originally Posted by ain

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);

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That is incomprehensible, try explaining what you are really trying to do, or provide more context please.

CB

Quote:

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Originally Posted by CaptainBlack

That is incomprehensible, try explaining what you are really trying to do, or provide more context please.

CB

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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.