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# lecture_3 - 16.333: Lecture #3 Frame Rotations Euler Angles...

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16.333: Lecture #3 Frame Rotations Euler Angles Quaternions

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Fall 2004 16.333 3–1 Euler Angles For general applications in 3D, often need to perform 3 separate rotations to relate our “inertial frame” to our “body frame” Especially true for aircraft problems There are many ways to do this set of rotations - with the variations be based on the order of the rotations All would be acceptable Some are more commonly used than others Standard: start with the body frame ( x, y, z ) aligned with the inertial ( X, Y, Z ), and then perform 3 rotations to re-orient the body frame. Rotate by ψ about Z x , y , z Rotate by θ about y x , y , z Rotate by φ about x x, y, z Euler angles: ψ Heading/yaw θ Pitch φ Roll
Fall 2004 16.333 3–2 Can write these rotations in a convenient form: ⎤⎡ x 0 X X y = 0 ⎦⎣ Y = T 3 ( ψ ) Y z 0 0 1 Z Z x 0 x x y = 0 1 0 y = T 2 ( θ ) y z 0 z z x 1 0 0 x x y = 0

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## lecture_3 - 16.333: Lecture #3 Frame Rotations Euler Angles...

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