Lecture 3 Notes Frame Rotations - Lecture 3 Notes Frame...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 re-orient 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) ⎣...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern