Day 4.2 - Rotation About y-axis ^ z0 ^ z1 ^ ^ y0 y1 ^ x0 ^...

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Rotation About y-axis 1/17/2011 6 0 ˆ x 1 0 ˆ ˆ y y 0 ˆ z 1 ˆ x +'ve rotation 1 ˆ z
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Relative Orientation Example 1/17/2011 7 0 ˆ x 1 0 ˆ ˆ z y 0 ˆ z 1 ˆ x 1 ˆ y 45
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Successive Rotations in Moving Frames 1/17/2011 8 1. Suppose you perform a rotation in frame {0} to obtain {1}. 2. Then you perform a rotation in frame {1} to obtain {2}. What is the orientation of {2} relative to {0}? ? 0 2 R 0 ˆ x 1 ˆ z 1 ˆ x 1 0 ˆ ˆ y y 0 ˆ z 2 ˆ x 2 1 ˆ ˆ z z 1 ˆ x 1 ˆ y 2 ˆ y 2 ˆ x 2 ˆ y 0 ˆ z 0 ˆ x 0 ˆ y 2 ˆ z , 1 2 z R R , 0 1 y R R
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Successive Rotations in a Fixed Frame 1/17/2011 9 1. Suppose you perform a rotation in frame {0} to obtain {1}. 2. Then you rotate {1} in frame {0} to obtain {2}. What is the orientation of {2} relative to {0}? ? 0 2 R 0 ˆ x 1 ˆ z 1 ˆ x 1 0 ˆ ˆ y y 0 ˆ z 1 ˆ x 1 ˆ z 0 ˆ y 1 ˆ y 2 ˆ x 2
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Day 4.2 - Rotation About y-axis ^ z0 ^ z1 ^ ^ y0 y1 ^ x0 ^...

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