MATLAB CODE NEEDED !! Starts with a given inertia matrix for a satellite and out

Question

MATLAB CODE NEEDED !!

Starts with a given inertia matrix for a satellite and outputs this matrix (with a label and units). Calculates and outputs the principal MOIs (with a label and units). The given inertia matrix is I^A = [3700 -400 -150 -400 5800 200 -150 200 8800] (kg m^2) where A is the arbitrary coordinate system used when the satellite was being designed. Calculates and outputs the DCM C^BA that transforms from the principal axis system B to system A (include a label). The appropriate Matlab commands are: [evec, eval] = eig(IA); e1 = evec(1, l); % extracts column 1 of the evector matrix e2 = evec(1, 2); % extracts column 2 e3 = cross(e1, e2); % creates new column vector e3 = el x e2 C_BA = [e1, e2, e3]; % form the DCM using the eigenvectors as the columns Calculates and outputs (with labels and units) the angles between the arbitrary axes and the principal axes: alpha = (a_1, b_1) beta = (a_2, b_2) theta = (a_3, b_3) A gyro sensor that measures angular velocity of the satellite is aligned with the A axes. At some time, the sensor is measuring omega^A = [0.4 0.5 0.8] (rad/s) Calculate and output the components of angular velocity in the principal axis system B (with a label and units).

Explanation / Answer

2)

i=[3700 -400 -150;-400 5800 200;-150 200 8800]

[axes,moments]=eig(i)

0utput:

i =

        3700        -400        -150

        -400        5800         200

        -150         200        8800

axes =

    0.9836   -0.1768   -0.0347

    0.1788    0.9813    0.0706

    0.0216   -0.0757    0.9969

moments =

    3.6240         0         0

         0    5.8566         0

         0         0    8.8194

6)

for clculting similarity transformation

1.find eigen values of the matrix

2eigen vector of the matrix

3.B- using eigen vectors

4.invrese B

5. invrese B*A*B

Matlab code:

T=balance(sys.I)

sysb=ss2ss(sys,inv(T))

ss2ss:performs similarity transformation

1)

The inertia matrix calculation is an additive operator.the inertia matrix of a body with two volumes V1+V2 is the sum of the inertia matrix of V1 and the inertia matrix of V2.

Methods for calculationg:

1.look-up tables

2.computer calculation: digital or symbolic

3. experiments

5)

with(linalg)

euler=vector([phi,theta,Wai])

deuler=vector([phi,theta,Xi])

we define matrix operators

Rz=matrix[[cos,sin,0],[-sin,cos,0],[0,0,1]);

Rx=matrix[[1,0,0],[0,cos,sin],[0,-sin,cos]

omega[phi]=vector[0,0,phi(t)];

omega[Theta]=vector[theta(t),0,0]

omega=evalm(A&*omega[phi]+Rz(Xi(t)&* omega{theta]+vector([0,0,xi(t)]))

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