MAE 6245 (Spring 2022) Robotic Systems Assignment # 1
Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit
MAE 6245 (Spring 2022)
Robotic Systems
Assignment # 1
1) For the given frames (0 and 1), find the rotation matrix specifying the orientation of frame 1 relative to frame 0.
[3 points]
2) Show that the dot product of two free vectors does not depend on the choice of frames in which their coordinates are defined. [Hint: use the definition of the dot product (xTx)] [5 points]
3) Imagine two unit vectors, v1 and v2, embedded in a rigid body. Note that, no matter how the body is rotated, the geometric angle between these two vectors is preserved (i.e., rigid-body rotation is an "angle-preserving" operation). Use this fact to give a concise (four- or five-line) proof that the inverse of a rotation matrix must equal its transpose and that a rotation matrix is orthonormal. [5 points]
This proves orthonormality as well.
4) 2 points awarded to anybody who has indicated their topic of interest.
2022-05-05