In case it is helpful, here are all the Flight Mechanics videos in a single playlist kzfaq.info/sun/PLxdnSsBqCrrEx3A6W94sQGClk6Q4YCg-h. Please let me know what you think in the comments. Thanks for watching!

AE512: Interesting to see the breakdown of translation and rotation in a single matrix, I've usually performed the operations separately but nice to see you can easily perform successive transformations.

AE512: Great lecture. I was able to do the homework following this step by step.

AA516: Good video! Augmenting the matrix makes total sense after seeing the composite transformations

AE 512 Very impressive the measurements on the board matched the mathematical calculations, nice steady drawing skills.

AE 512: great video prof. Lum

AE512: Great lecture, especially the 3D example. Really helped put things into perspective with different objects with different reference frames (translationally/rotationally) and how to relate them all together via transformation matrices.

AE 512: Nice lecture, the physical examples with measurments definitely help with my understanding, thanks!

AA516: Allie S, this is really neat! I haven't thought about this type of transformation being possible and I am excited to learn even more uses for it.

- no questions; just wanted to say I'm so thankful you derived the 2D case and extended it to 3D instead of directly deriving the 3D case :)

AA516: I was going to ask this in Office Hours but I believe I figured it out. For anyone that might be wondering in 33:10 why the rotation matrix is different from what we learned in the past rotation lecture (Flight Mech 02), it is because the rotation from frame b to frame 1 is left handed! That is why it is transposed/inversed.

AA516: Forgot to comment on this when I watched it the first time but great video! These types of transformations were super interesting and I was excited to go more indepth

AE512: I absolutely love your real world examples and enthusiasm

AA 516 - You made it real easy to understand by Developing the homogeneous transformation in 2D and then doing the Extension to 3D. Great explanation on material as always!

AA516: Even though the reference frames started adding up, it still was easy to follow and see how powerful the homogeneous transformation matrix is.

AE 512 - Great video. Sketches of frames/coordinate systems and inclusion of numerical examples were extremely helpful in making the material 'stick.'

AA516 - I really like how you incorporate real-world examples into these lectures. It really helps me grasp the material

AA516 - So far I really appreciate Prof. Lum's lecture styles with various real world/computaitonal examples. Looking forward to learning more lectures!

AA 516: Great video, very informative lecture.

AA 516: Another great lecture! Glad to see that our aircraft can start flying around instead of only rotating in one place and excited for what comes next.

AA 516: One of my favorite lectures so far. Doing a multi-stage chain transformation like this has always been something I thought about particularly in regard to air combat with all of the sensor and radar data that gets distributed between aircraft, and has been something I wish I could do on a variety of projects. Very excited that I understand the fundamentals behind this process!

AA 516 - Great Lecture

AE512: It's amazing how someone can keep all of these building blocks in mind while trying to create a dynamic simulation where this is only one small part.

Good topic, I'm also very much into spatial transformations atm.

AE512: now I won't be confused when I hear a GNC engineer talk about 'pose'!

AA516: Very useful!

AE512: During a rigid body dynamics calculation, I have previously done something where I used a combination of a vector addition and rotation matrices to accomplish something similar. I think this could have expedited my workflow.

Really enjoying your videos, hope to get through each one. I did find one thing confusing though, as may others. In a previous video, "Expressing Vectors in Different Frames Using Rotation Matrices", when a vector is known in Fr and desired in F1, the angle Theta was calculated in the RHS from Fr to F1, resulting in [cos(theta) sin(theta); -sin(theta) cos(theta)]. In this video, the rotation from Fb to F1 was [cos(alpha) -sin(alpha); sin(alpha) cos(alpha)] as the result of the angle being defined as the RHS angle from F1 to Fb. If the angle was from Fb to F1 as in the prior video, the prior rotation matrix could be used. Wolfram Mathworld uses [c(psi) s(psi); -s(psi) c(psi)] where psi is the RHS angle from the reference frame to the rotated frame, as in your first video. Do you have a preference as to how the angle is defined?

tnku so much sir

AA516 : Cool how successive transformations stack on top of each other.

AE512: these transformations keep building on eachother and getting more complicated! I think you’re doing a great job breaking it down piecewise though.

Jason-AE512: This is helpful to understand the homework question 1

AE512: at 46:30, why do you measure theta from x2 to xr all the way around? In the previous case, x1 to xr, it was the smaller angle. Why is it different here (why do we not measure from xr to x2)?

AA 516: On the last statement made in the video, when you went to the 3D rotation and translation matrix, what if the target reference frame was at two different rotation ie a different psi and theta

sir can you upload dynamics also like forces and moments

AE512: Thanks Dr. Lum! Off the top of your head, do you have any resources for how to concatenate matrices in mathematica? I think it might be easier to build up the zeta matrix one piece at a time, and put it all together!

AA516: Hi professor! The video is great as always. At 19:00 min, we used r(t/b) frame 1 instead of frame r (reference frame). Is that because r(t/b) origin aligns with frame 1? (Daniel Teshome) Thank you!

Question : @16:14 Please correct me if i am wrong. The rotational matrix C1/b(psi) from Fb to F1, shouldn't the psi in the -ve direction since the Z^r is coming out of the plane?

A A 516: Ojasvi Kamboj

AE512: I wondered what is the maximum frames that someone had been developing in the real world using this transformation matrix method.

[AE 512] 42:40 You are drawing the vector from car to origin because you have to keep the vector addition "tip to tail". Basically, however many vectors you add, you have to make sure they are tip to tail to keep the equations valid?

AA516 are there other applications of this transformation where we could expand to dimensions greater than 3D?

Are you sure you wrote that rotation matrix wrong at 16:38? It looks like the same type of rotation in your video Expressing Vectors in Different Frames Using Rotation Matrices at 19:16 in that video. It is a right hand angle, rotating from the reference frame to a 1 frame. If the angle is positive, it looks like what you wrote is correct, or matches the other video.

[AE 512]: @16:41 you say that C_1/b is a 2x2 rotation matrix with the angle being psi, where psi is defined as FROM the 1 axes TO the b axes. However, we want to rotate FROM the b axes TO the 1 axes, so isn't the rotation matrix as you've defined it here incorrect? Shouldn't C_1/b actually be the transpose of what's on the board?

AA 516: Celeste Yuan

AA 516, no questions

???? why are there so many letters, and what does this have to do with physical posistions

AE512

AA516

"I dont wanna get the s i g n of s i n wrong" hahaha (thr goes my 1st ever comment in yt) 33:59