Stability Analysis, State Space - 3D visualization

[@EugeneKhutoryansky]

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[@thevikingwarrior]

How can I make a video like this? I know that I need things like Blender. I wanna use my computer to make videos like you are. What sort of things do you have to do? How do you get people to view them and so on. Tell me all about what you have done to make this happen?

[@fakherhalim]

I cannot think of any other 24 minutes video ON THE PLANET that can explain systems' stability so clearly! I wish I could recommend your channel for an AWARD! You guys really understand Physics and Math!

[@EugeneKhutoryansky]

Thanks for that really great compliment.

[@feynstein1004]

He's just a guy, actually. Not guys. :)

[@fakherhalim]

That is incredible. I thought it would be a team of people -- carefully planning, doing all the math, preparing through chores of simulations, and final presentations -- just unbelievable amount of work so nicely done just by a single guy!

[@99Gara99]

@@fakherhalim Eugene can be a he or a she

[@brunocalhiari976]

@@99Gara99 by the voice I guess it is a she...

[@RahulSharma-oc2qd]

you should be given some sort of award for having that much determination to help out a section of students.... Kudos !!!!!

[@EugeneKhutoryansky]

Thank you.

[@anjishnu8643]

Stable, unstable and marginally stable explained through eigenvalues altered my entire perception of control systems. Extremely grateful for your videos.

[@pranayreddy6033]

one of the most underrated KZbin channels.

[@EugeneKhutoryansky]

Thanks for the compliment.

[@ganeshr3493]

pranay reddy r u here cuz of control systems?

[@dabdoube92]

the*

[@memebandit]

I love you @pranay reddy

[@EugeneKhutoryansky]

If you like this video, you can help more people find it in their KZbin search engine by clicking the like button, and writing a comment. Thanks.

[@godsadog]

I am currently highly interested in equilibria, especially in dissipative systems. I was SO excited seeing your novel video regarding equilibrium points. Thanks!

[@sensualarmpit3512]

new vid by eugene. its almost like connecting to an actual presence. it gets me motivated, gets me elevated, gets me to another dimension. aint nothing like it. you know what i mean. you know what im saying? i could vape to that bruh

[@TheFirstBK]

I know what you're saying

[@alejandrodpg]

Physics Videos by Eugene Khutoryansky, commenting is the least we can do to thank you for your exceptional legacy!

[@cameronspalding9792]

If a differential equation has positive eigenvalues: then it’s unstable: like d^2 y/dx^2 =y then it’s unstable

[@bloggervista]

thanks eugene for redefining what education should be

[@EugeneKhutoryansky]

Thanks.

[@robinranabhat3125]

fuck you bajgai

[@nomestoni]

Impressive! I remember you mentioning on a comment that you were preparing this video, and I was waiting for this moment. Your videos are of an amazing quality and personality!! Thank you

[@EugeneKhutoryansky]

Thanks for the compliment about my videos.

[@mohammedhammad2113]

Woooaah! This is GOLD! I am not even finished with the video but just can't resist thanking the creator. BEST!!

[@EugeneKhutoryansky]

Thanks. I am glad you liked my video.

[@TheChrasse]

There is no better start for the day than drinking my morning coffee and watching Eugene's newest video.

[@EugeneKhutoryansky]

Glad to provide people with a happy start to their day. :)

[@mnada72]

As alway ... genus explanation and demonstration for the topic .... this the first time that I know what is the use of eigenvalues and eigenvectors...I hope your videos span over all scientific topics so that no more misunderstanding or lack of understanding.

[@mnada72]

After 2 years, seems like the first time. What a pity 😕

[@johnhippisley9106]

How incredible of an insight to represent the state of an insight as a vector in a space. Now geometry can be used to solve these complicated problems! Who had this revelation?

[@firelow]

this is just too interesting. when I saw the complex eigenvalue with a negative real part I just screamed "ITS THE HELICOPTER"

[@pronounjow]

The helicopter is the positive real part.

[@senthilkumaranmahadevan6531]

I have never come across such a stunning explanation which gives such an insight to the Eigen vectors and stability. Dear Eugene Khutoryansky you are a real teacher ........ Great. your contribution to the intellectual society is great great great I petty those who disliked this video. As a teacher i see the quality of work. brilliant

[@EugeneKhutoryansky]

Thanks for the compliments.

[@EugeneKhutoryansky]

You can help translate this video by adding subtitles in other languages. To add a translation, click on the following link: kzbin.info_video?ref=share&v=p9qrHdPEe28 You will then be able to add translations for all the subtitles. You will also be able to provide a translation for the title of the video. Please remember to hit the submit button for both the title and for the subtitles, as they are submitted separately. Details about adding translations is available at support.google.com/youtube/answer/6054623?hl=en Thanks.

[@ffhashimi]

This is without a doubt one of the best scientific channels in KZbin; You always keep impress us with your videos ! Thanks for this great video and for all of your work.

[@EugeneKhutoryansky]

Thanks for the compliment.

[@acho8387]

I got an adrenaline rush when I saw your new video in the sub feed.

[@feynstein1004]

Lmao dude

[@Kabitu1]

My brain always gets a semi when I see a new video

[@stevo322222]

I check your channel daily for new videos. I especially like the one's explaining space-time. Great job!

[@EugeneKhutoryansky]

Thanks. By the way, if you subscribe to my channel, you can set up your KZbin settings so that you will get an automatic email notifying you each time I upload a new video.

[@VeganSemihCyprus33]

One of the high quality useful content channels on youtube. Keep them coming! :)

[@UifaleanAlexandru]

THIS IS SIMPLY AMAZING! Nobody has been able to provide such a deep intuition! Well done.

[@EugeneKhutoryansky]

Thanks for the compliment about my video.

[@ArvindRao33455]

Very well explained. Thanks for showing us the easy yet effective way of learning tricky physical concepts that would have otherwise be rote learned if restricted to the text book.

[@EugeneKhutoryansky]

Thanks. I am glad you liked my explanation.

[@adrianperez1404]

this is incredible I have such a more clear understanding of the relationship between eigenvalues and stability. you're doing a great service to us Eugene thank you so much

[@EugeneKhutoryansky]

Thanks.

[@mateusheinenfeltrin2474]

OMG, you are the best professor in the world

[@EugeneKhutoryansky]

Thanks for the compliment.

[@AJ-et3vf]

Awesome video about state-space representation! Immensely lucid and greatly represented, allowing one to have an intuition of the concepts involved. The music is also calming and engaging. Great work!

[@EugeneKhutoryansky]

Thanks for the compliments. I am glad you liked my video.

[@feynstein1004]

Amazing video. The wait was totally worth it. Can't wait for more videos from you, Eugene. You're an inspiration to me. :)

[@dude8309]

this has to be one of the most educational videos on youtube.. so clear and understandable

[@EugeneKhutoryansky]

Thanks for the compliment about my videos.

[@ZombieSS77]

This seems like a great introduction to the underlying concepts of control theory for LTI systems. This made some great connections for me. It now makes much more sense that poles in the left half plane of a root locus plot mean the system is stable and how the math is used to move right half poles to the left side. I knew that piece of knowledge, but didn't understand it until now.

[@motaaaa]

This is better than a whole semester of classes in a university

[@EugeneKhutoryansky]

Thanks for the compliment about my video.

[@minasalehi2023]

Great! I always wondered why on earth we should have these two equations and now I realize! thank you so much

[@EugeneKhutoryansky]

Thanks. I am glad my video was helpful.

[@OfAbram]

Thank you Eugene for helping me understand and become excited about many of the intuitions and underlying mathematics behind simple and complex ideas.

[@EugeneKhutoryansky]

Thanks.

[@VlanimationTales]

Lovely explanation of equilibrium positions! The eigenvalues add a whole new dimension to the thought process. 😊

[@EugeneKhutoryansky]

Thanks. I am glad you liked my explanation.

[@VlanimationTales]

@@EugeneKhutoryansky You're welcome! 😉

[@leoberges1705]

Your video reaches as always such a level of perfection, it is so beautiful, from the music and the animation and mostly to the wonderful physics questions you raises. You are very good at making understandable this very odd way science describes the world now. Thank you a lot for that !

[@EugeneKhutoryansky]

Thanks for the compliment about my videos.

[@connemignonne]

I'm always so excited for new content from you, and this was particularly enlightening! Thankyou so much!

[@EugeneKhutoryansky]

Thanks. I am glad you liked my video.

[@kindpotato]

Oh yeah sick video. I just learned another application of complex numbers.

[@anandkumarpatidar1140]

I feel this is one of the most underrated channel.

[@EugeneKhutoryansky]

Thanks!

[@jaredcollette442]

Wonderful! I really enjoyed the explanation on how eigenvalues visually relate to stability. I've known the math for years but only now understand the visualization. Thank you! :)

[@EugeneKhutoryansky]

Thanks. Glad I was able to help you visualize it.

[@bowmanzz1]

This video is Bloody Ace's! Brilliant. As a left and right brained person this is all I need to understand why my homework is now correct. Thank you for making this.

[@EugeneKhutoryansky]

Thanks for the compliment about my video.

[@pendalink]

Fantastic video as usual! This reminds me that I think many students would find a video on partial derivative error propagation useful

[@khalidahmad1944]

The best channel on youtube. Thanks for the amazing video.

[@EugeneKhutoryansky]

Thanks for that really great compliment.

[@aishasyed9756]

Such an intuitive explanation. If you did a whole such course on math on Udemy etc., I would definitely pay to learn from it.

[@danielboisa]

Nice! Just perfect to understand stability!

[@EugeneKhutoryansky]

Thanks for the compliment.

[@christiancordeiro3030]

this was very well presented, really helps to know what im actually looking at

[@EugeneKhutoryansky]

Thanks. I am glad you liked my video.

[@christiancordeiro3030]

@@EugeneKhutoryansky I had a question about how a system can have 2 state vectors. So how can we have 2 blue and white vectors for the X1 and X2 plot. Appreciate any feedback.

[@EugeneKhutoryansky]

We have vectors for "X1" and "X2", and we also have vectors for "d(X1)/dt" and "d(X2)/dt."

[@christiancordeiro3030]

@@EugeneKhutoryansky I thought that the vector is a combination of X1 and X2 points, so how can do of those vectors exist at the same time

[@FingerThatO]

ahh. this would've saved my butt in Lagrange. Thanks for making it seem so simple.

[@hakankarakurt1100]

Real quality and effort making these videos. Thank you!

[@EugeneKhutoryansky]

Thanks for the compliment about my videos.

[@mrxbrk4624]

ALL VIDEOS ARE UTTERLY WONDERFUL. we're waitin' further ones

[@EugeneKhutoryansky]

Thanks for the compliment about my videos. More are on their way.

[@Mau365PP]

I wish my control system class was like this, Thank you!

[@EugeneKhutoryansky]

Glad you liked my video. Thanks.

[@smustavee]

The best youtube channel. I have fallen love with it. Best wishes for you

[@EugeneKhutoryansky]

Thanks for that really great compliment.

[@smustavee]

I feeling honored as you replied. I wish one day I can work with you

[@pravii444]

Pure Love towards teaching. Thanks for the explanation.

[@EugeneKhutoryansky]

Thanks.

[@engineerallen5156]

this is one of the best channels for knowledge

[@engineerallen5156]

actually i mean intelligence

[@EugeneKhutoryansky]

Thanks.

[@engineerallen5156]

how do you manage to make the animations? must take ages

[@EugeneKhutoryansky]

I make my 3D animations with "Poser."

[@engineerallen5156]

must take you hundreds of hours

[@teemo8247]

Wow! All of these things you shown makes sense!

[@EugeneKhutoryansky]

Glad to hear that.

[@ashwinsrinivas7278]

Useful for control engineering concepts which has state space analysis as a fundamental concept and requirement. Kindly do more on control engineering related concepts!! Such an abstract field requires such amazing and novel methods of presentations!! Only you can do this....

[@kanchanchauhankc]

😊All your videos are amazing.. have not seen such visualisation of concepts.. hats off to ur great effort.. the visualisation, voice, 3d effects, framing of concepts, everything is superb, it helped me a lot to understand the theortical things we always constrained to cram..Thanks a ton to make them so interesting...🙏🙂👌👌

[@EugeneKhutoryansky]

Thanks. I am glad you like my videos.

[@cript3232]

The animations are as well done as the explanations as always.

[@EugeneKhutoryansky]

Thanks for the compliment.

[@jameswilson8270]

Eugene Khutoryansky You make some sweet videos with awesome animations! However, I'm going to be a critic on this one because you did some things that could trip people up easily. The rest of this comment is addressed to Eugene, but it is really for the people who watched the video, got lost, but feel they shouldn't have. At 11:14, the axes changed to x1, x2, so that you were dealing with a 2x2 system of linear ODEs of the form (dx_1/dt; dx_2/dt) = A(x_1; x_2) instead of a 1x1. I did not notice that at first, so I was confused until I noticed the change. At 12:20, you could've explained how all linear combinations of the eigenvectors represent all states. Finally, starting at 16:46, even though you explicitly stated you were only showing a solution corresponding to one variable, it would have been better, in my opinion, to show all of the components of the solution on separate graphs. I imagine some people got immediately confused because it only showed one component (in this case the blue vector) of the solution. Technically, the blue vector you show is not the vector with eigenvalues (1/2)i and (-1/2)i. An eigenvector must contain all the variables of the system. The only other criticism I have is it would have helped students more effectively if you had shown more equations that explicitly show the things you were referring to. Other than that, you produced a very good and accurate video for people to learn from. Respectfully, James W

[@shezeeblanka1611]

this is an absolute gem.

[@EugeneKhutoryansky]

Thanks. I am glad you liked my video.

[@jimlbeaver]

Really great video. I always wondered how stability analysis was done. Thanks!

[@EugeneKhutoryansky]

Thanks. I am glad you liked my video.

[@Hustleandstack]

this channel is groundbreaking

[@EugeneKhutoryansky]

Thanks.

[@kipropkigz1285]

thank you for making me live math.. you don't just instruct, you let me experience

[@EugeneKhutoryansky]

Thanks.

[@DDDelgado]

Great explanation for linearity in a system

[@mrxbrk4624]

Every curious person seek for contents like these for free.

[@TonyStark-fh3iv]

Awesome videos and awesome content, what could one do to thank you. All I could do is hit on like, subscribe and quote a comment of thanks. Thank you very much for your effort... Keep explaining all the mathematical equations physically, what they really mean & let the world know they are not just for playing by substituting numbers..

[@ridiculous_]

the most wanted topic

[@maksudjonusmonov5711]

Wow, so much meaning in one video.

[@EugeneKhutoryansky]

Thanks.

[@11Petrichor]

Excellent information! Thank you! Looking forward to more:)

[@Xinvoker]

The Legend

[@nbyitsolutionbd]

This is really impressive. Nice work

[@EugeneKhutoryansky]

Thanks for the compliment.

[@mareialgarni2012]

Amazing explanation and visualization

[@EugeneKhutoryansky]

Thanks for the compliment.

[@majdwahbi44]

Perfectly explained! Thanks

[@EugeneKhutoryansky]

Thanks. Glad you liked my explanation.

[@realcygnus]

superb content........ as always

[@EugeneKhutoryansky]

Thanks for the compliment.

[@КостяЛисятка]

Great video and the greatest chanell about science. Your visualisations of differents phenomena of the nature, of laws of physics, of мathematical equations are very understandable and intelligible. Many concepts have become more clear for me. Your job is the art of education! If you can please make video abour automatic control systems

[@EugeneKhutoryansky]

Thanks for the compliment. I did talk a little about automatic control systems in this video, though I may also do more videos on this topic in the future. Thanks.

[@ZombieSS77]

Math becomes intuitive once you realize what it represents! I didn't like math until I started learning physics. Have you considered tackling the Einstein Field Equations? The visualizations of tensors and differential geometry would make the scary looking math click for so many people.

[@EugeneKhutoryansky]

Yes, I would like to eventually do a video on Einstein's Field Equations. Thanks.

[@alexjimenez6020]

Amazing graphic explanation!!

[@EugeneKhutoryansky]

Thanks.

[@sandorszabo2470]

The music is also excellent.

[@walfluca]

You are the best man,thank you for your work!

[@EugeneKhutoryansky]

Thanks. I am glad you liked my video.

[@markfinn825]

I figure I am now far enough beyond the best part being long gone to want to know the name of the tune that goes with this video (rather than only take it for granted). But as far as I have mostly gotten lately is stacks of strings of memory cells could have made a kid seem cool enough to find a girl while the above statement was far enough in the future not to worry about much. Another topic to consider is how this thing that seems to skip a beat can count and can be used to switch which of two memory cells is connected to the input of what its now part of and which output the (memory cells) are connected to as well as erasing one on time to use it to memorize what's at the input next. And how that memorizing , switching , erasing concept has other uses as well . Other than that these videos with their elevating etc. images set to that kind of music and the way the narrator speaks are really pieces of work to be admired.

[@bustersverden4689]

Beautiful video!

[@EugeneKhutoryansky]

Thanks. I am glad you liked my video.

[@AhnafAbdullah]

Amazing video! At first it looks simple but increases in complexity rapidly D:

[@EugeneKhutoryansky]

Glad you liked my video.

[@ionutzasaftei1989]

Your videos are extraordinary, you are a specialist ! :)

[@EugeneKhutoryansky]

Thanks for the compliment. I am glad you like my videos.

[@ionutzasaftei1989]

They are awesome, we are waiting for more videos, smart people always love physics ! :)

[@fredericbastiat5502]

Superb as always!

[@EugeneKhutoryansky]

Thanks for the compliment.

[@R3DPandaLP]

you make the complicated seem simple

[@EugeneKhutoryansky]

Thanks.

[@EdneiBloemer]

absolutely LOVE your videos, keep it up!

[@alphablondy04]

finally back!

[@nayanmitra3714]

You are simply awesome. I wanna get more video on mathematics.

[@EugeneKhutoryansky]

Thanks. More videos on all topics, including mathematics, are on their way.

[@RoboBoddicker]

I'm glad you mentioned autorotation. I was cringing in anticipation of the angry helicopter pilots in the comments :D

[@DDDelgado]

7:06 when the deviations from any equilibrium point are small, any non-linear system can be appoximated to a linear one, pretty good, I do electrochemical impedance, this is always the asumption.

[@DrPepper776]

i fall asleep to these videos :)

[@glutinousmaximus]

Well, the "heavy object on a rubber sheet" analogy is okay as far as it goes. It allows us to visualize *_one_* tiny slice of how gravity is affecting space around the object. The problem is, that all of the space around the object _cannot_ be visualized. Never mind.

[@Jakenheimer1]

I love this channel

[@EugeneKhutoryansky]

I am glad to hear that. Thanks.

[@cameronspalding9792]

@4:06 this is like when you have a 2nd order differential equation where the auxiliary equation has 2 complex roots: both with a positive real part

[@अण्वायुवरीवर्त]

Yeah Like underdamped vibrations

[@Lucky10279]

So can we think about equilibrium points on terms of energy needed to cause a change? A non-equilibrium point would require energy to _stop_ the ball from moving, a non-stable equilibrium point would require very little energy to cause it to move and a stable point would require more energy to get it moving.

[@jairoandresguevarajulio571]

It was a very useful explanation. Thank's.

[@EugeneKhutoryansky]

Glad you liked my explanation. Thanks.

[@hasankaynak2253]

very clear explanation. thank you very much.

[@EugeneKhutoryansky]

Thanks. I am glad you liked my explanation.

[@Flitampare]

Are you a telecommunication engineer or have any relation whith it? All the stuff in this channel (Calculus, Algebra, Physics, Electric Circuits , Electromagnetism, Fourier Analysis... etc) is completly related whith this carreer (which im studing). Im just curious to know :P I love your videos by the way! you do such a great work and it helps me a lot whith my studies. Keep it up!

[@sebandrescastillo]

Que buen video lpm

[@prashannashrestha9791]

too much love for your video...thank you

[@EugeneKhutoryansky]

Glad you liked my video.

[@cabbler]

I would love a video about centripital forces and universal gravity

[@bdedi]

best channel

[@EugeneKhutoryansky]

Thanks for the compliment.

[@ZYTUSA]

You're videos are so illuminating! What do you use to make these graphics? WebGL?

[@EugeneKhutoryansky]

I make my 3D animations with "Poser." Thanks for the compliment.

[@dittoma]

So, eigenvalues tell you the equilibrium of a system Real part = How much the object will move away from equilibrium Imaginary part = how quickly it will oscillate

[@drmichaelhz]

just perfect explanation :)