Register to reply 
Rotation matrix 
Share this thread: 
#1
Mar3012, 03:57 AM

#2
Mar3012, 06:29 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,497

Rotation about the xaxis through angle [itex]\alpha[/itex] is given by the matrix
[tex]\begin{bmatrix}1 & 0 & 0 \\ 0 & cos(\alpha) & sin(\alpha) \\ 0 & sin(\alpha) & cos(\alpha)\end{bmatrix}[/tex] Rotation about the yaxis through angle [itex]\beta[/itex] is given by the matrix [tex]\begin{bmatrix}cos(\beta) & 0 & sin(\beta) \\ 0 & 1 & 0 \\ sin(\beta) & 0 & cos(\beta)\end{bmatrix}[/tex] Rotation about the zaxis through angle [itex]\gamma[/itex] is given by the matrix [tex]\begin{bmatrix} cos(\gamma) & sin(\gamma) & 0 \\ sin(\gamma) & cos(\gamma) & 0 \\ 0 & 0 & 1\end{bmatrix}[/tex] The result of all those rotations is the product of those matrices. Be sure to multiply in the correct order. 


#3
Mar3012, 09:49 AM

P: 677

I suspect that there's a minus sign somewhere wrongly placed in your matrices Halls, am I correct? I moved the minus sign in your second matrix to the lower sine but there's still something wrong for this is my result:



#4
Mar3012, 10:23 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,497

Rotation matrix
No, all of the minus signs are correctly placed. I am, of course, assuming that a positive angle gives a rotation "counterclockwise" looking at the plane from "above" from the positive axis of rotation.



#5
Mar3012, 10:36 AM

P: 677

But the wiki page shows a different position for the minus sign of your second matrix:
http://en.wikipedia.org/wiki/Rotation_matrix. 


#6
Mar3012, 12:56 PM

Mentor
P: 15,153




Register to reply 
Related Discussions  
Rotation matrix  Advanced Physics Homework  0  
Shankar 12.4.4  the rotation matrix vs. a rotation matrix (tensor operators QM)  Advanced Physics Homework  2  
Rotation matrix vs regular matrix  Linear & Abstract Algebra  5  
Construct a rotation matrix out of another rotation matrix  General Math  2  
How do you use a Rotation Matrix in 2D?  Introductory Physics Homework  3 