Vector Derivatives (the Equation of Coriolis) and the Angular Velocity Vector

In this video we develop the Equation of Coriolis which describes how a vector in a rotating reference frame changes from the perspective of an observer in a non-rotating reference frame. We will see that this is related to the angular velocity vector describing the relative motion of the two frames. As such, we also investigate some properties of this angular velocity vector.

Topics and time stamps:
0:00 – Introduction
0:41 – Example using an aircraft
9:11 – Diagrams of body frame, reference frame, and vector in question
17:25 – Picture-in-picture showing vector derivative from body frame’s perspective
19:55 – Picture-in-picture showing vector derivative from reference frame’s perspective
24:45 – Derive Equation of Coriolis using Rodrigues’ Rotation Formula
42:35 – Derive Equation of Coriolis using small angle analysis
1:03:26 – Properties of the angular velocity vector
1:11:13 – Summary and conclusions

Lecture notes and code can be downloaded from https://github.com/clum/YouTube/tree/...

References:
-Stevens, B. L. and Lewis, F. L., “Aircraft Control and Simulation, 2nd Edition”, John Wiley and Sons, 2003, pg. 9-10.
-Blakelock, J., “Automatic Control of Aircraft and Missiles”, John Wiley & Sons, Inc., 1965, pg. 296.
-Expressing Vectors in Different Frames Using Rotation Matrices (   • Expressing Vectors in Different Frame...  )
-Derivation of Rodrigues’ Rotation Formula (   • Derivation of Rodrigues’ Rotation For...  )
-Velocity & Acceleration in Non-Inertial Reference Frames (Coriolis & Centrifugal Acceleration) (   • Velocity & Acceleration in Non-Inerti...  )

All Flight Mechanics videos in a single playlist (   • Flight Mechanics  )

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