In case it is helpful, here are all the Flight Mechanics videos in a single playlist kzfaq.info/sun/PLxdnSsBqCrrEx3A6W94sQGClk6Q4YCg-h. You can support this channel via Patreon at www.patreon.com/christopherwlum. Please let me know what you think in the comments. Thanks for watching!

AE512: Super helpful to go through the derivation of the Rodrigues Rotation Formula, especially having the two different views of the circle. And how we were able to determine the desired vector based on a piece meal formulation of more or less projections in the frame we wanted.

AA516 Good one, I always love imagining rotating vectors. Ever since calc 3 doing volume integrals of rotated lines - the mental image is so cool.

Great walkthrough of the derivation, thanks.

Great derivation - It's fun to see things fall into place!

AA516: Came back for a rewatch, I appreciate the coding in matlab in the end, the graphic really helped

AA516: Forgot to comment on this when I watched it the first time but really great to see all the steps broken down into easy to digest parts

AA516: I liked how you took what seemed to be a complicated derivation and spent time in the beginning breaking down what we we're really looking at and what we needed to solve for. This made it wayyy easier to follow and understand.

you are the great prof of this century, huge thanks sir

AA 516: I enjoyed following the derivation and thought the props at the beginning did a great job illustrating what was happening in 3D.

AA516: The real-life model was helpful. Looking forward to seeing how this formula is used.

AA516: Great, thoroughly description of such an important tool

In depth derivation, easy to follow along with

Amazing! Wow you truly show your passion for teaching. Thanks so much!

AA 516: Great to see detailed steps on the derivation

omg, this is such a complete explanation for angle axis rotation. thank you so much

Handy new formula with many applications!

Thank you so much for taking time out of your life so that we get a better understanding of the field we are pursuing. Utmost respect.

Thank you very much for your effort. Both the derivation of the formula and the MATLAB demonstration were perfect :)

AE512: Learned something new today. Thanks!

Very nicely explained, helped a lot. Thank you!

AA 516: Clear lecture, was able to follow each step easily!

AE 512 The 3D example with the pvc pipes and labels was a useful visual to setting the stage for the formulation.

AE 512: The color coding and drawings in multiple perspectives makes this long derivation much easier to follow. Great video!

Great video! Super clear and informative -- definitely helped me out. Thanks!

pausing the video just to appreciate how well you have explained everything. you sir saved a life.

This is amazing!!! Thank you so much for putting this together. As someone who does engineering as a hobby, resources like this are invaluable. So clear and easy to understand.

AE512: Words can't describe how helpful the props are in explaining these concepts, thanks for going the extra mile 🙂

AA516: Great lecture video! You explained the Goldstein rotation formula more in depth than what is mentioned in the book and I really apreciate your visualizations with the pipes and MatLab simulation. Thanks Professor!

Amazing! proficient explanation!

thanks for the lecture!

Excellent. Thank you!

I liked the derivation on the board. I also liked the part where you showed my eyes what was happening with matlab. But my favorite part was the transition at 42:22

Great derivation!

AE 512 Cool formula, very useful!

Lum老师会说中文吗？ Dr.lum is the teacher I dream to have in the math and physical class of the highschool, detailing the steps and rediscovering the inherent beauty of mathematics. Thank you! It is really helpful.

Nice and clear derivation

AE512: this one was a bit harder to follow than the prior two videos as I got a little lost in all the linear algebra notation. The Matlab show and tell sections are very helpful in helping me understand what’s going on.

AE512: Very interesting concept, seems similar to the foundations of a quaternion, wonder how much influence these concepts had on each other

Interesting derivation

AA516 very clear explanation

AE512: It's crazy how many different building blocks underly flight mechanics, this being one of them.

AA 516 Very easy to understand

Chris, your videos are great, any suggestions with respects to books that follow your material?

AE512: Thanks for the great visuals/diagram! Is this formula related to quaternions?

AE 512: This was a great and easy to follow derivation. I am a little confused on how/when this will be applied in this course. An example of that would be nice throughout the lecture.

Jason-AE512: The matlab part help me understand the material better.

Thanks a lot :)

AA 516: This was an awesome video, I really appreciate the visuals. I'm curious, what is so special about making it a left handed rotation (since almost everything we do is right handed)? I assumed that would be arbitrary because switching it just adds a negative, but wondering if there was something more to it.

AE512: I found the Rodrigues derivation easy to follow. I noticed that the lecture notes in the github was only the cover page when I downloaded it. Maybe there was an error in the upload?

AA 516: Celeste Yuan (Late due to name discrepancies discussed)

AA516: Shows many applications in orbits with multiple reference frames

great video sir why can't express vector NW as (cos Mu ) and vector WV as( sin Mu) ?

AA 516: Are we going to use this left-hand rotation version for all of our analyses in the future instead of the right-hand rotation?

Just messing about. First day using 'Octave' (don't have Matlab), so apologies for the code. Super lectures, thank you very much. If one tries.... %Start of Script clear clc close all %Define unit vector n = [1;0;1]; n = (1/norm(n))*n; %n needs to be unit vector %define vector U u = [2;2;-1]; %Does not need to be unit vector %define range of angles of rotation mu_range =linspace(0,2*pi,50); %rotate u around vector a figure % Moved code JL clf legend ('u','n','v') xlabel('x') ylabel('y') zlabel('z') grid on title('Rotation of u around n') axis equal view([32 15]) axis([-norm(n)-2 norm(n)+5 -norm(n) norm(n)+5 -norm(n)-5 norm(n)+5]) %Slightly changed JL % End Moved code JL %Var to signal first time plotted JL VOldSet=0; for i=1:length(mu_range) %clf; %Added JL if (VOldSet==1) %If has been plotted then cover with white (with outline) plot3([0 VOld(1)],[0 VOld(2)],[0 VOld(3)], 'w-','Linewidth', 2); endif hold on %Get the current rotation angle mu=mu_range(i); %Apply Rodrigues rotation of a vector, formula (Equation 1.2-6 in %Stevens and Lewis) v = (1 - cos(mu))*dot(n,u)*n + cos(mu)*u - sin(mu)*cross(n,u); %Draw u plot3([0 u(1)],[0 u(2)],[0 u(3)], 'r-','Linewidth', 2); %Draw n plot3([0 n(1)],[0 n(2)],[0 n(3)], 'g-','Linewidth', 2); %Draw v plot3([0 v(1)],[0 v(2)],[0 v(3)], 'b-','Linewidth', 2); %Keep old V plot - Set flag for above.... VOld=v; VOldSet=1; ## legend ('u','n','v') ## ## xlabel('x') ## ylabel('y') ## zlabel('z') ## ## grid on ## title('Rotation of u around n') ## axis equal ## ## view([32 15]) ## axis([-norm(n) norm(n) -norm(n) norm(n) -norm(n) norm(n)]) drawnow pause(0.1); %Pause for animation end %End of Script

AA516 : Cool Matlab Script!

very easy to follow the derivation!

AE512: You mention at 28:10 that we have to add d as a unit vector to "give this thing a direction". The cross product yields a vector, not a scalar, so it already has a direction, right? Does multiplying by d just scale the resultant cross product vector such that it results in a magnitude of 1? If that's the case, then could another mathematically identical way of doing this be (instead of multiplying by d) to divide |u| |n| sin(phi) by the magnitude of |u| |n| sin(phi)?

Marker revealed @7:05

AE512: Thanks for the detailed derivation! One question - why do Stevens and Lewis (and Goldstein) use the left hand rule? Comparing to other sources on the internet, Rodrigues appears to use the right hand rule, which causes a sign switch on the sine term (en.wikipedia.org/wiki/Rodrigues%27_rotation_formula)

this files associated with this lecture(pdf) what can i be downloaded ?

interesting

Might have been interesting to see what happens in MATLAB when n is not a unit vector.

Ojasvi Kamboj - AA 516

Carter loves winglets

AE512

AA 516

I'm just here so I won't get fined.

AE512