2B11  Transformation Matrix Between Two Coordinate Systems

 

Consider two systems   .  Now we are interested in obtaining     from using a rigid body rotation of  .  We are also interested to relate the unit vectors  in  from that of 

 

We see that    

 

  is the transformation given  by 

 

 

We note that for , is an orthogonal matrix

 

                        (e.g.) 

 

For example