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Unformatted text preview: Lecture 3 Notes: Frame Rotations • 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 reorient the body frame. ① Rotate by ψ about Z ⇒ x , y , z ② Rotate by θ about y ⇒ x , y , z ③ Rotate by φ about x ⇒ x, y, z Euler angles: – ψ ∼ Heading/ yaw – θ ∼ Pitch – φ ∼ Roll • Can write these rotations in a convenient form: ⎡ x ⎤ ⎡ cψ ⎣ y ⎦ = ⎣ − sψ z sψ 0 ⎤⎡ X ⎤ ⎡ X ⎤ cψ 0 ⎦⎣ Y ⎦ = T 3 (ψ) ⎣ Y ⎦ 0 1 Z Z ⎡ x ⎤ ⎡ cθ ⎣ y ⎦ = ⎣ z sθ 0 − sθ ⎤⎡ x ⎤ ⎡ x ⎤ 1 0 ⎦⎣ y ⎦ = T 2 (θ) ⎣...
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 Fall '14
 JonathanP.How
 Angular Momentum, Rigid Body, Rotation, Euler angles, body frame

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