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That's awesome! Thanks for watching!!

You're welcome! Thanks for watching.

Welcome Braulio! It's great to learn of your background and that you enjoy the course content. The next lesson will appear tonight if all goes to plan!

Hey Joseph, q is pitch rate and qbar is dynamic pressure. Correct on z_e. Thanks for watching!

Hello there! Yes, folks can access the code through support of the channel on Patreon. It's 5 bucks a month and you get all codes, as well as additional content that helps explain the codes. www.patreon.com/user?u=86359827

Right, L means you have a linear problem. You can get a solution for a nonlinear problem statement but you may have to resort to numerical results, as opposed to an analytical solution.

Thank you! I'm glad you like them.

You got it, more coming soon!

Thanks!

Hey Kevin, the basis is that zero los rate means the target is at a constant lead angle relative to the pursuer so that if the closing velocity is positive, there will be a collision. If the los rate is nonzero, then one body will pass the other. The exception is if the target constantly maneuvers. Then there will be necessary a changing los rate for intercept, up to intercept.

Thanks for catching those bugs!

Hi there, absolutely! Tabular drag data for a body is often given as a function of Mach number. To find the data, you'll have to search in reports, journal articles, or conference papers through your favorite search engine. As I find good resources for aerodynamic data, I'll link to them on the webpage, www.learngandc.com.

Doing some research for an upcoming video, I found this report that you may find helpful: ntrs.nasa.gov/api/citations/20110016614/downloads/20110016614.pdf

@@LearnGandC thank you. It seems that best fit curves for Cd across a range of Mach numbers are usually derived from a collection of drop test results. I wonder if someone has devised a mathematical approach of getting Cd values based on object dimensions.

Yes, the dimension comes in from computing drag from the drag coefficient as the reference area is involved. In addition, there is the transition to turbulence, a Reynolds number effect, which is based on diameter.

No problem! Thanks for watching!

@@LearnGandC why not animating the results next time with matplotlib it would give a huge value and better understanding of what is happening when running the simulation 🙋🏻

Yes, eventually I will do this. Further, I plan to interface with Flight Gear to really bring things to life. All in time.

@@LearnGandC that's great and more comprehensive, thank you sir 😊🙏🏻

There are a lot of topics in this one for sure! It's great to know you appreciate it. Thanks

You're welcome. I made this series after I found very limited explainations of the principles of guidance and also in response to the silly "the missile knows where it is..." video.

​@@LearnGandC doesn't mean anything to me or maybe I'm too dumb to understand the missile knowing where it is in that video.

It was determined from the inverse tangent of the crossrange over downrange from the relative position vector at t(i+1). These positions were literally measured on the diagram to determine lambda(i+1).

You are correct! Another viewer also found this error a couple years ago. I have a list of errata in the video description. Thanks for watching!

Thanks for catching that! I take it you meant great course as opposed to great curse haha

Hello, Codes are available to Patreon subscribers ( www.patreon.com/user?u=86359827 ). The model is in its early stages of development, but once completed, it absolutely could be used as a RL agent.

Absolutely! Trim is a question of whether an aircraft can hold an equilibrium at a flight condition. About that equilibrium condition, the system can be stable or unstable.

@@LearnGandC I have a nonlinear aircraft model. When I trim the aircraft for stable case (Cg ahead of the neutral point) there is no problem, but when I move Cg behind the neutral point again I can find a trim point but aircraft cannot maintain its trim condition. Even I run the simulation for 1-2 seconds, aoa increases by 2-3 degrees for example (system has no disturbance or perturbation). Also, I used simulink for this simulation. Do you have any idea what should be the reason sir?

Yes, what you are experiencing is normal and expected. First, note that you have an unstable dynamic system. Second, note that you are attempting to simulate that system with an initial condition about its equilibrium point. However, ask yourself, do you know exactly the equilibrium (trim) condition? If your system diverges its because your off the equilibrium condition. The difference between your approximated trim condition and the exact trim condition may be small, but that small difference will grow according to the severity of the instability.

@@LearnGandCI understand what you mean. Thank you very much for your answer and videos.

You're welcome

Thanks very much! I've just started developing the next lesson.

@@LearnGandC Can't wait. One thing I would love to see here is how can we use this simulation, to spec out our actuators? I know we need more information regarding flight path and conditions, but that would be fantastic. Cheers.

Thank you! I'm looking forward to publishing the next one.

I'm very happy to get this one published! You're welcome. Thank you for watching and engaging.

@@LearnGandC can't wait for the next one, so we can add aerodynamic forces and moments 🤩💯

Thank you, I enjoy making these lessons.

Thanks, the next lesson is almost finished!

@@LearnGandC can't wait ☺️

Thanks for catching that. It's good to know at least one person is working through the material! In my code, I believe I had it correct so all results should reflect -a and not 1-a.

To be clear, the result of the partial fraction expansion should be: 1/(p*-p)/(s+p) + 1/(p-p*)/s+p*) right?

Thanks for the feedback

It's a great sign that you find this interesting as a first year student in Engineering Physics. I appreciate the good words and wish you the best in your academic career and beyond. More content is coming soon!

Glad you liked it!

+2 for Python.

Check out this lesson: th-cam.com/video/CMOh2xWk_qA/w-d-xo.html

@@LearnGandC Thank you!

Python is working out great!

I appreciate that. I'm looking forward to developing this simulation further.

Thanks! Next thing I know some flat-earther will be twisting my video.

@@LearnGandC I was thinking that, too.

Thank you.

My pleasure

The ZEM PN shown in this lesson is equivalent to linearized True PN. Check out Section 4 Module 1 for details. Both Pure and True laws are effective, but the data each law requires has implications to sensor selection and filtering.

@@LearnGandC Hi adding on to his question. Is there a reason why your lessons focus so much on ZEM pro nav? Is it because it's linearized and easier to analyze? I would like to implement 3D pro nav and I would like to understand the non ZEM ways to do it and decide on the best one for my use case. My chaser is a drone where I have 3D velocity and acceleration control along with yaw rate control. My sensors are IMU for own drone kinematics and camera to estimate target kinematics. In my case I believe it is easier to calculate LOS rate than ZEM and time to go. May I request a lesson on 3D pro nav using LOS rate? I would appreciate that alot and thank you.

I'm looking forward to finishing the first lesson

They are certainly related, but quadrotors are outside my present domain. Sorry, no references. Good luck!

Yes, you can use Matlab's built in solver interchangeably. It's great to know you like the content. Thanks

Thanks, I'm thinking Python!

alright, I code in C++. I think I could translate standard code lines, but will appreciate your help when I am stuck

The plan is to code throughout as I don't own a personal Simulink license.

Hi Nicholas! I expect the vehicle model definition to be several lessons. For aero data, I expect to find a published report from which I'll go through explaining the coefficients, their coordinate systems, and the force and moment build-up. The process of translating data in a report into something useful is not often covered.