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2. Compute the equivalent Euler angles. WARNING: It is forbiden to use the Matlab library function eul2rotm here. Pay attention to the unit: degree, as well as in trigonometric functions. a. Given R1, compute the successive w-u-w angles: angle w, angle u, angle_w1. R1 = [0.0629 0.9101 0.4096 -0.9559 -0.0629 0.2868; 0.2868 -0.4096; 0.8660]; angle_u = 0 angle w = 0 angle_w1 = 0 b. If the same R1 is realized by the rotations around body frame axes, as follows: First rotates around w by aw, then around v by av, and finally around u by au. Compute the three successive angles aw, av, and au, respectively. av = 0 au = 0 aw = 0 c. The body frame firstly coincides with the fixed frame, then it has the following successive rotations all about the body frame axis: Rotation about w by angle. W, rotation about u by angle u, rotation about w again by angle_w1, rotation about w by aw, rotation about v by av, and finally rotation about u by au. Compute the final rotation matrix R2. R2 = zeros(3,3) d. If the above R2 is only realized by three successive rotations by roll, pitch and yaw aroud the fixed frame axes x, y and z, compute the roll, pitch and yaw. pitch = 0 roll = 0 yaw = Ө

2. Compute the equivalent Euler angles. WARNING: It is forbiden to use the Matlab library function eul2rotm here. Pay attention to the unit: degree, as well as in trigonometric functions. a. Given R1, compute the successive w-u-w angles: angle w, angle u, angle_w1. R1 = [0.0629 0.9101 0.4096 -0.9559 -0.0629 0.2868; 0.2868 -0.4096; 0.8660]; angle_u = 0 angle w = 0 angle_w1 = 0 b. If the same R1 is realized by the rotations around body frame axes, as follows: First rotates around w by aw, then around v by av, and finally around u by au. Compute the three successive angles aw, av, and au, respectively. av = 0 au = 0 aw = 0 c. The body frame firstly coincides with the fixed frame, then it has the following successive rotations all about the body frame axis: Rotation about w by angle. W, rotation about u by angle u, rotation about w again by angle_w1, rotation about w by aw, rotation about v by av, and finally rotation about u by au. Compute the final rotation matrix R2. R2 = zeros(3,3) d. If the above R2 is only realized by three successive rotations by roll, pitch and yaw aroud the fixed frame axes x, y and z, compute the roll, pitch and yaw. pitch = 0 roll = 0 yaw = Ө

International Edition---engineering Mechanics: Statics, 4th Edition
International Edition---engineering Mechanics: Statics, 4th Edition
4th Edition
ISBN:9781305501607
Author:Andrew Pytel And Jaan Kiusalaas
Publisher:Andrew Pytel And Jaan Kiusalaas
Chapter9: Moments And Products Of Inertia Of Areas
Section: Chapter Questions
Problem 9.43P
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2. Compute the equivalent Euler angles. WARNING: It is forbiden to use the Matlab library function eul2rotm here. Pay attention to the unit: degree, as well as in trigonometric functions. a. Given R1, compute the successive w-u-w angles: angle w, angle u, angle_w1. R1 = [0.0629 0.9101 0.4096 -0.9559 -0.0629 0.2868; 0.2868 -0.4096; 0.8660]; angle_u = 0 angle w = 0 angle_w1 = 0 b. If the same R1 is realized by the rotations around body frame axes, as follows: First rotates around w by aw, then around v by av, and finally around u by au. Compute the three successive angles aw, av, and au, respectively. av = 0 au = 0 aw = 0
Transcribed Image Text:2. Compute the equivalent Euler angles. WARNING: It is forbiden to use the Matlab library function eul2rotm here. Pay attention to the unit: degree, as well as in trigonometric functions. a. Given R1, compute the successive w-u-w angles: angle w, angle u, angle_w1. R1 = [0.0629 0.9101 0.4096 -0.9559 -0.0629 0.2868; 0.2868 -0.4096; 0.8660]; angle_u = 0 angle w = 0 angle_w1 = 0 b. If the same R1 is realized by the rotations around body frame axes, as follows: First rotates around w by aw, then around v by av, and finally around u by au. Compute the three successive angles aw, av, and au, respectively. av = 0 au = 0 aw = 0
c. The body frame firstly coincides with the fixed frame, then it has the following successive rotations all about the body frame axis: Rotation about w by angle. W, rotation about u by angle u, rotation about w again by angle_w1, rotation about w by aw, rotation about v by av, and finally rotation about u by au. Compute the final rotation matrix R2. R2 = zeros(3,3) d. If the above R2 is only realized by three successive rotations by roll, pitch and yaw aroud the fixed frame axes x, y and z, compute the roll, pitch and yaw. pitch = 0 roll = 0 yaw = Ө
Transcribed Image Text:c. The body frame firstly coincides with the fixed frame, then it has the following successive rotations all about the body frame axis: Rotation about w by angle. W, rotation about u by angle u, rotation about w again by angle_w1, rotation about w by aw, rotation about v by av, and finally rotation about u by au. Compute the final rotation matrix R2. R2 = zeros(3,3) d. If the above R2 is only realized by three successive rotations by roll, pitch and yaw aroud the fixed frame axes x, y and z, compute the roll, pitch and yaw. pitch = 0 roll = 0 yaw = Ө
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