Computing Euler Angles: The Euler Kinematical Equations and Poisson’s Kinematical Equations

In this video we discuss how the time rate of change of the Euler angles are related to the angular velocity vector of the vehicle. This allows us to design an algorithm to consume measurements from a rate gyro and compute the resulting Euler angles of the vehicle.

Topics and Timestamps:
0:00 – Introduction and demonstration
8:53 – Deriving the Euler Kinematical Equations
38:44 – Example
46:23 – Simulink implementation of the Euler Kinematical Equations
1:02:57 – Poisson’s Kinematical Equations
1:14:01 – Simulink implementation of Poisson’s Kinematical Equations

#FlightMechanics

[reesetaylor]

AE 512: I appreciate the physical demonstrations of how to interpret the difference between the rate gyro output and the euler angles, really helped solidify my understanding

[ShivaShakerii]

AA 516: Excellent presentation, Professor Lum! I was particularly impressed by the way you derived the block diagrams of the processes. Great job!

[WalkingDeaDJ]

Jason-AE512: That simulink is good way to practice.

[BryanLiberman]

AE512: Hey Dr. Lum, thanks for making this video! Content like this can get very complicated, and you presented it in a way that made it (comparatively) easy to follow!

[sunnysarkar]

AE 512: Doing the simulink with us is extremely helpful and useful. I am glad that is being included.

[jordantriolo]

AE512: Great video! I appreciated the Simulink portion, letting us see how the equations could actually be used.

[newschool]

I spent weeks searching for how to convert IMU values to Euler and all I got was bunch of formulas and no explanation. Especially thank you for explaining difference between IMU values and Euler rate and Euler angles.

[prabhjeetsingharora]

It is totally worth spending time refreshing the basics of Flight mechanics taught in the BEST possible manner. Each day I am going through at least one video of this channel, which has greatly enhanced my knowledge. Once again, thankyou Dr. Lum for creating such a beautiful content.

[benjaminshipp]

You're an outstanding educator! I really appreciate your level of effort and care you put into ALL of your videos. Not only do you have a clear grasp on this tough subject, but you are able to communicate it with clarity and ease. You have a rare gift Sir!

[yaffetbedru]

AA516: I enjoyed the examples and the you bringing physical hardware to show during the lecture. Really ties the ends together.

[davidtelgen]

AE512: Great video with the simulink examples!

[matthewbajamundi]

AE 512 I found the Simulink portion very insightful to how the Kinematical equations can be implemented using actual data from a sensor.

[milesrobertroane]

AA516: Great video as always! I love watching Mathematica chow down on some horrible equations that I would've gasped at when I was a freshman.

[kktousif]

Excellent lectures Mr. Christopher. Indeed easy to follow and fall in love with the subject.

[edwardmau]

AE 512
Thanks for the Simulink demonstration.

[charlesperry]

A very effective lecture. The explanation and the presentation of the relavant eauations are in sync.
Unlike other video s on the same subject , lecturers keep on talking without pointing to with eauations
he is talking about. Many eauation and figures are.dumped all over the slide in one slide.

[ramenegg]

I could understand the stuff with this video clearly, which I have struggled with it multiple days.

[sethwhittington]

AE512: the possibility to have an error occur in the model of the aircraft reaches certain attitudes makes me nervous. This is the thing I will always forget to take into account! 😮

[rowellcastro]

AA516: Hello Professor! Another great lecture! You explained very well how a flight controller could take in IMU data expressed from the body frame and convert it to readable data expressed in the reference frame that we see in a telemetry screen from GUI software such as Ardupilot. Thank you very much.

[NicAqueous]

By far the best explanation on this topic. Great work!