euler angles, method of direction cosines and quaternions for alpha = 30,45,60 deg

clc;

alpha = 45
omega = 30
lam = 0.0001

p = omega*cos(alpha)
q = 0
r = omega*sin(alpha)
%%integration equations from pg 356
%%method of direction cosines
c11=1
c12=0
c13=0
c21=0
c22=1
c23=0
c31=0;
c32=0
c33=1

cd11=c12*r-c13*q
cd12=c12*p-c11*r
cd13=c11*q-c12*p
cd21=c22*r-c23*q
cd22=c23*q-c21*r
cd23=c12*q-c22*p
cd31=c32*r-c33*q
cd32=c33*p-c13*r
cd33=c31*q-c32*p

theta = asind(-c31)
phi = acosd((c33/sqrt(1-(c31^2)))*c32)
psi = acosd((c11/sqrt(1-(c31^2)))*c21)

%%Euler angles
phid=p+r*tan(theta)*cos(phi);
thetad=-r*sind(phi)
psid=r*sec(theta)*cos(phi)

%%quaternions
e0 = cos(psi/2)*cos(theta/2)*cos(phi/2)+sin(psi/2)*sin(theta/2)*sin(phi/2)
e1 = cos(psi/2)*cos(theta/2)*sin(phi/2)-sin(psi/2)*sin(theta/2)*cos(phi/2)
e2 = cos(psi/2)*sin(theta/2)*cos(phi/2)+sin(psi/2)*cos(theta/2)*sin(phi/2)
e3 = -cos(psi/2)*sin(theta/2)*sin(phi/2)+sin(psi/2)*cos(theta/2)*cos(phi/2)

E= 1-(e0^2+e1^2+e2^2+e3^2)

ed0=(-1/2)*(e1*p+e2*q+e3*r)+lam*E*e0
ed1=(1/2)*(e0*p+e2*r-e3*q)+lam*E*e1
ed2=(1/2)*(e0*q+e3*p-e1*r)+lam*E*e2
ed3=(1/2)*(e0*r+e1*q-e2*p)+lam*E*e3

Answer 1

[James Tursa]

What is your question? If you want to check conversions between quaternions, direction cosine matrices, and Euler angles, I would suggest this FEX submission by John Fuller:

http://www.mathworks.com/matlabcentral/fileexchange/20696-function-to-convert-between-dcm--euler-angles--quaternions--and-euler-vectors

Also, review this tutorial:

http://www.mathworks.com/matlabcentral/answers/6200-tutorial-how-to-ask-a-question-on-answers-and-get-a-fast-answer

[srina nair]

I am unable to get the graph. i want to know how to perform ode45 to integrate phid in the above coding