4. For a given rotation matrix as following, [ru 112 113 Rx(O) = 21 122 123 L'31 32 V 32 V 33 describe an algorithm that

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4 For A Given Rotation Matrix As Following Ru 112 113 Rx O 21 122 123 L 31 32 V 32 V 33 Describe An Algorithm That 1 (141.65 KiB) Viewed 28 times

4. For a given rotation matrix as following, [ru 112 113 Rx(O) = 21 122 123 L'31 32 V 32 V 33 describe an algorithm that extracts the equivalent angle and axis of a rotation matrix as shown in Equation (2.80). k.k ve+cokk,vo-k se k k ve+k, 50 cᎾ kyk– so R, (O)=k, k, vo+k_so k,k,vo+co k,k_vo – k_so (2.80) k_k_vo – k,so k,k_vo + k_so k_k_vo + co Equation (2.82) is a good start, but make sure that your algorithm handles the special case 0 = 0º and 0 = 180°. X ху x AK O = Ar cos lu + 122 + 133 Po -1 2 132–123 1 113-131 2. sine L21 -'12 (2.82) Hint: The inverse algorithm consists of three sub-algorithms: a) If 0=0°, lct 0=0°, calcualto (2.80) and solving for 4K =[K, K, K.] b) If 0=180°, let 0=180°, calcualte (2.80) and solving for 4K =[K, K, K:] c) Otherwise, using (2.82) x y x