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Homework 06 - Rotation parameterization by quaternions

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).

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