# Solve For T?

• Aug 29th 2011, 12:42 AM
ain
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))
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);
• Aug 29th 2011, 06:57 AM
CaptainBlack
Re: Solve For T?
Quote:

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))
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
• Aug 29th 2011, 08:17 AM
Ackbeet
Re: Solve For T?
Quote:

Originally Posted by CaptainBlack
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.