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Homework 06 - Rotation parameterization by quaternions

Task

In Maple:

  1. Verify that formula (7.74) in PRO-2012-Lecture-12.pdf for quaternion composition holds true.
  2. Verify that formula (7.76) in PRO-2012-Lecture-12.pdf for quaternion composition holds true.
    1. Find the quaternion representation r1 and matrix representation R1 of the rotation by Pi/2 around x-axis.
    2. Find the quaternion representations quaternion representation r2 and matrix representation R2 of the rotation by Pi/2 around y-axis.
    3. Construct the quaternion representations r21 of the rotation r21 = r2 o r1 using the composition 'o' of quaternions.
    4. Find the rotation matrix R21 = R2.R1 by matrix multiplication '.'.
    5. Construct the rotation matrix from r21 and compare it to R21.
    6. Construct the quaternion from the rotation matrix R21 and compare it to r21. (Hint: R→axis & angle→quaternion).

Upload

Upload via the course ware the zip archive hw06.zip containing

  1. hw06.mws Maple script (functions) solving the assignment.
  2. hw06.pdf description of the solution (algorithms, results, comments).
courses/pro/labs/hw06.txt · Last modified: 2018/09/03 17:27 (external edit)