3. (50 points) Considering the cube based on the notation of a standard American dice described in Fig. 2, the number la

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3 50 Points Considering The Cube Based On The Notation Of A Standard American Dice Described In Fig 2 The Number La 1 (63.84 KiB) Viewed 30 times

3. (50 points) Considering the cube based on the notation of a standard American dice described in Fig. 2, the number labeled on each face of the dice is arranged such that the sum of the number on the opposite face and itself is equal to 7. To illustrate this fact, let us define an inertial frame (fixed global frame) OXY Z and a body frame Ox’yºz' attached onto the dice. Initially, they are both aligned with each other as shown in Fig. 2(a). If we rotate the dice about the Z axis of the inertia frame with 180 degrees, you will see the face with number '6aligning with the X axis of the inertia frame (Fig. 2(b)). If we start with the orientation of the dice as shown in Fig. 2(a). Determine the new orientation of the dice (A=?, B=?, C=?) in Fig. 2(e) after the following rotations: Y. X.X (a) Case 1 (C) Case 3 (b) Case 2 Figure 2. Frame descriptions (a) (20 points) Perform an Euler angle rotation in the order of axes z'; y';z' with angles -90°; +90°; -90° (b) (20 points) Perform a fixed angle rotation in the order of axes 2; Y; Z with angles -90°; +90°; -90° (©) (10 points) Are these two results identical? If no, can you suggest a set of rotation pattern for the fixed angle rotation that results the same orientation as shown in the part (a)? If yes, what can you learn from the above two different cases?