Solution2 - AE 321 Solution of Homework #2 1(a) Note that...

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AE 321 – Solution of Homework #2 1(a) Note that we are rotating the original frame counterclockwise by 30 degrees. Therefore, ° + = 30 θ . The rotation matrix R has the form '' ' 11 12 13 21 22 23 31 32 33 (1.1) cos sin 0 sin cos 0 0, 3 (vertical axes coincide) 00 1 3/2 1/2 0 1/2 3/2 0 1 0 1 T T ii T xx xx xx Rx x x x x x xxxx xx i θθ α ⎡⎤ ••• ⎢⎥ =• ⎣⎦ == = = =− 30° 30° x 1 x 1 x 2 x 2 x 3 , x 3 1(b) In this part of the problem, we are performing two successive rotations. Let’s denote the rotation matrix for the first rotation as and that for the second rotation as . 1 R 2 R 1
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45° 45° x 1 x 1 x 2 x 2 x 3 , x 3 x 2 x 1 ’,x 1 ’’ x 3 x 2 ’’ x 3 ’’ 60° 60° Applying Equation (1.1) to the first rotation, we get = = = 1 0 0 0 2 / 2 2 / 2 0 2 / 2 2 / 2 1 0 0 0 2 / 2 2 / 2 0 2 / 2 2 / 2 1 0 0 0 45 cos 45 sin 0 45 sin 45 cos 1 T T R Applying Equation (1.1) to the second rotation, we get = = = 2 / 1 2 / 3 0 2 / 3 2 / 1 0 0 0 1 2 / 1 2 / 3 0 2 / 3 2 / 1 0 0 0 1 60 cos 60 sin 0 60 sin 60 cos 0 0 0 1 2 T T R Combining the two above rotations to get the total rotations, =
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This note was uploaded on 01/18/2010 for the course AE 321 taught by Professor Waller during the Fall '07 term at University of Illinois at Urbana–Champaign.

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Solution2 - AE 321 Solution of Homework #2 1(a) Note that...

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