Question

3) Given the following quaternions, calculate the equivalent DCM matrices, 3-2-1 Euler Angle Sequences, and resulting rotated vector v2 after rotating vector v1 = (1, 0, 0) with each q. Hint: If you do it in MATLAB you don't have to repeat the whole process each time. a) q = [0.7071, 0, 0, 0.7071] b) q = [0, 0.7071, 0, 0.7071] c) 9 = [0, 0, 0.7071, 0.7071] d) q = (-0.7071, 0, 0, 0.7071]

Answer 1

Given quaterions are

a.) q=[0.7071, 0, 0, 0.7071]

b.) q=[0, 0.7071, 0, 0.7071]

c.) q=[0, 0, 0.7071, 0.7071]

d.) q=[-.7071, 0, 0, 0.7071]

a.) q=[0.7071, 0, 0, 0.7071]                      

• Equivalent DCM Matrices for given quaterion :

         0    1.0000         0
   -1.0000      0            0
         0         0    1.0000

• 3-2-1 Euler Angle Sequence for given quaterion :

1.57079632679490   0   0

• Resulting Rotating vector v2 after rotaing vector v1=[1,0,0] for given quaterion :

0   -1.00000000000000   0

b.) q=[0, 0.7071, 0, 0.7071]

• Equivalent DCM Matrices for given quaterion :

         0         0    1.0000
         0   -1.0000         0
    1.0000       0           0      

• 3-2-1 Euler Angle Sequence for given quaterion :

0   -1.57079632679490   0

• Resulting Rotating vector v2 after rotaing vector v1=[1,0,0] for given quaterion :

0   0   1.00000000000000

c.) q=[0, 0, 0.7071, 0.7071]

• Equivalent DCM Matrices for given quaterion :

   -1.0000      0            0
         0         0    1.0000
         0    1.0000         0   

• 3-2-1 Euler Angle Sequence for given quaterion :

3.14159265358979   0   1.57079632679490

• Resulting Rotating vector v2 after rotaing vector v1=[1,0,0] for given quaterion :

-1.00000000000000   0   0

d.) q=[-.7071, 0, 0, 0.7071]

• Equivalent DCM Matrices for given quaterion :

         0   -1.0000         0
    1.0000      0            0
         0         0    1.0000

• 3-2-1 Euler Angle Sequence for given quaterion :

-1.57079632679490   0   0

• Resulting Rotating vector v2 after rotaing vector v1=[1,0,0] for given quaterion :

0   1.00000000000000   0

%% MATLAB CODE %%

clc;                                                                                    % Clear Command Window
clear ;                                                                                % Clear Workspace Variable
close all;                                                                            % Close Windows of MATLAB

q=zeros(4,4);                                                        % Creating zeros Matrix 4 rows * 4 column
q(1,:)=[0.7071, 0, 0, 0.7071];                                               

q(2,:)=[0, 0.7071, 0, 0.7071];

q(3,:)=[0, 0, 0.7071, 0.7071];

q(4,:)=[-.7071, 0, 0, 0.7071];

%% Equivalent DCM Matrices for given quaterions %%
DCM = quat2dcm(q);                                                            % Convert Quaterion to DCM

%% 3-2-1 Euler Angle Sequence for given quaterions %%
Euler=quat2eul(q);                                                                % Convert Quaterion to DCM

%% Resulting Rotating vector v2 after rotaing vector v1=[1,0,0] for given quaterions %%

v1=[1,0,0];
v2=quatrotate(q,v1);                                                              % Rotate Vector v1 for given Quaterion