[3] 2 Find the rotation of point p =5 by 60 about the axis u =...

   

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[3] 2 Find the rotation of point p =5 by 60 about the axis u = -2. - - 1 a. Using quaternions. b. Using the rotation matrix. Note the rotation matrix R for rotation by an angle 8 about the axis [x] u = |uy| having | |u|| = u+ u+ u = 1 is given by: [u] cos8+ u(1-cos 8) R = Uxuy (1 - cos 8) + u sin 8 uzux (1 - cos 6) - uy sind UxUy (1 - cos 8) - uz sind cos8 + uz (1 - cos 8) uyuz (1-cos 8) +ux sin d 2 c. Compare the R matrix for rotation around u = -2 by S = 60 with R(0; 0;) to determine - 1-] U, uzux(1- cos 8) + uy sin d Uyuz (1 - cos 8) - ux sin d cos & + u(1 cos 8) the corresponding roll, pitch, and yaw angles. [3] 2 Find the rotation of point p =5 by 60 about the axis u = -2. - - 1 a. Using quaternions. b. Using the rotation matrix. Note the rotation matrix R for rotation by an angle 8 about the axis [x] u = |uy| having | |u|| = u+ u+ u = 1 is given by: [u] cos8+ u(1-cos 8) R = Uxuy (1 - cos 8) + u sin 8 uzux (1 - cos 6) - uy sind UxUy (1 - cos 8) - uz sind cos8 + uz (1 - cos 8) uyuz (1-cos 8) +ux sin d 2 c. Compare the R matrix for rotation around u = -2 by S = 60 with R(0; 0;) to determine - 1-] U, uzux(1- cos 8) + uy sin d Uyuz (1 - cos 8) - ux sin d cos & + u(1 cos 8) the corresponding roll, pitch, and yaw angles.