I have Rotation Matrix, I want the order of the rotation angle by angle

Discussion in 'MATLAB' started by Carlos Junior, Apr 1, 2011.

1. Carlos JuniorGuest

Hi,
I would like to put a subject on the table to the friends of the Forum that I have a suspection how to do, but the way I think is a bit complicated!

The DOUBT: I have a rotation matrix 3x3 with all the 9 elements known and I would like to know the order of rotation and the angles of rotation.

The practical example:
v = [ 0.245 ; -0.563 ; -0.055 ] ;
u = [ 0.3 ; -0.5 ; -0.2 ] ;

v = R * u ;
And R is found to be:
R =[ 0.9766 0.1555 0.1487 ;
-0.0887 0.9208 -0.3797 ;
-0.1960 0.3576 0.9131 ] ;

My idea to solve the doubt:
There are 12 possibilities of order of rotation : ( theta_x,theta_y,theta_z ),( theta_x,theta_z,theta_y ),( theta_y,theta_x,theta_z ),( theta_y,theta_z,theta_x ),( theta_z,theta_x,theta_y ),( theta_z,theta_y,theta_x ) and the more possibilities: ( theta_x,theta_y,theta_x ),( theta_x,theta_z,theta_x ),( theta_y,theta_x,theta_y ),( theta_y,theta_z,theta_y ),( theta_z,theta_x,theta_z ),( theta_z,theta_y,theta_z ) .
My idea to know the angles and order of rotation of matrix R (the origin of the matrix) is to test one by one the 12 possibilities shown above with the nine elements of matrix R and eliminate the possibilities that returns incoherences. But, I think it is not a smart method and I think it can return me more than one possibility.

Is there a way to know the unique angles and order of rotation of matrix R ?

Very thanks,

Carlos

Carlos Junior, Apr 1, 2011

2. Matt JGuest

==============

You will not find that 1 out of the 12 possibilities are correct. All 12 possibilities are equally valid, but result in different theta_x,y,z.

Matt J, Apr 1, 2011

3. Bruno LuongGuest

The order must be decided by YOU.

Bruno

Bruno Luong, Apr 1, 2011
4. Carlos JuniorGuest

Yes, Bruno is correct . I can decide the order I want of rotation and then find theta_x,theta_y and theta_z, based on the matrix R and its nine elements found before!

I will post, here, the angles I found for all the 12 rotation possibilities to help who reads this post with a numerical (practical) example...

Only a correction: the value of the vector u should be u = [ 0.3 ; -0.5 ; +0.2 ] ; and not u = [ 0.3 ; -0.5 ; -0.2 ] ; as I have posted above !

Very Thanks one more time Bruno ...

Carlos Junior, Apr 1, 2011
5. James TursaGuest

See this conversion tool by John Fuller in the FEX:

http://www.mathworks.com/matlabcent...cm-euler-angles-quaternions-and-euler-vectors

James Tursa

James Tursa, Apr 3, 2011
6. Husam AldahiyatGuest

Husam Aldahiyat, Apr 3, 2011