Register to reply 
How to find angle after two rotations 
Share this thread: 
#1
Jan2313, 06:29 PM

P: 1,302

I have coordinate system A with bases a, b, c.
Say I rotate the whole system 30 degrees, so that the angle between a and a' is 30 degrees. Then I make another rotation so that this plane of rotation is perpendicular to that of the old one. What is the angle between a and a' now? I am trying to find the angles to use in a tensor transformation law, but I am having problems understanding what the angles will be between the old and new axes when a transformation isn't just a single rotation in one plane of the system. Tia 


#2
Jan2413, 06:55 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,552

You can write any rotation as a matrix multiplication. Then two rotations is given by the product of the two matrices.
For example, if you wrote 30 degrees around the z axis, the rotation is given by [tex]\begin{bmatrix} cos(30) & sin(30) & 0 \\ sin(30) & cos(30) & 0 \\ 0 & 0 & 1\end{bmatrix}= \begin{bmatrix}\frac{\sqrt{3}}{2} & \frac{1}{2} & 0\\ \frac{1}{2} & \frac{\sqrt{3}}{2}& 0 \\ 0 & 0 & 1\end{bmatrix}[/tex] A rotation around the yaxis, through 30 degrees is given by [tex]\begin{bmatrix} cos(30) & 0 &sin(30)\\ 0 & 1 & 0 \\ sin(30) & 0 & cos(30) \end{bmatrix}= \begin{bmatrix}\frac{\sqrt{3}}{2} & 0 & \frac{1}{2} \\ 0 & 1 & 0 \\ \frac{1}{2} & 0 & \frac{\sqrt{3}}{2}\end{bmatrix}[/tex] The two rotations together would be given by the product of the two matrices. 


#3
Jan2413, 06:58 AM

Sci Advisor
HW Helper
Thanks
P: 26,148




Register to reply 
Related Discussions  
Axis angle rotations and changing rotation values  Linear & Abstract Algebra  3  
Bullet Strikes Wheel  find rotations/second  Introductory Physics Homework  6  
Find angle of incidence given deviation angle  Introductory Physics Homework  6  
Javelin throw, find time it takes for angle one to change to angle two  Introductory Physics Homework  1  
Zero angle launch problem: Find height given inital speed and angle  Introductory Physics Homework  1 