7.3 Introduction to transformation matrices

This problem was contributed by Thomas Uchida at the University of Ottawa.

Frame A and point lie on the plane :

Note that unit vector is pointing out of the screen. The coordinates of point are (2.1, 0.5, 0) when expressed in frame A. Frame B lies in the same plane and has the orientation shown below:

(a) Find the rotation matrix that relates the orientation of frames A and B. Use any strategy to check your answer and explain why it is correct.

(b) For part (b) only, suppose the origins of frames A and B are coincident. Use your answer from part (a) and the expression to compute . Recall that rotation matrices are orthogonal, which means that .

(c) Now suppose the origin of frame B is at relative to the origin of frame A. What is the transformation matrix that relates frames A and B?

(d) Use your answer from part (c) and the expression below to compute :

(e) Sketch frame A, frame B, and point to confirm that your answer to part (d) is correct.

Solution (only visible by instructors; please contact us to request access)

Unable to render {include} The included page could not be found.