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...

[@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!

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[@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

[@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

[@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 😕

[@anjishnu8643]

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

[@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.

[@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. :)

[@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.

[@bloggervista]

thanks eugene for redefining what education should be

[@EugeneKhutoryansky]

Thanks.

[@robinranabhat3125]

fuck you bajgai

[@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.

[@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.

[@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.

[@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.

[@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.

[@mateusheinenfeltrin2474]

OMG, you are the best professor in the world

[@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

[@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.

[@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

[@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.

[@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.

[@VeganSemihCyprus33]

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

[@feynstein1004]

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

[@kindpotato]

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

[@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.

[@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.

[@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.

[@danielboisa]

Nice! Just perfect to understand stability!

[@EugeneKhutoryansky]

Thanks for the compliment.

[@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.

[@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! 😉

[@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.

[@motaaaa]

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

[@EugeneKhutoryansky]

Thanks for the compliment about my video.

[@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.

[@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.

[@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.

[@khalidahmad1944]

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

[@EugeneKhutoryansky]

Thanks for that really great compliment.

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

[@anandkumarpatidar1140]

I feel this is one of the most underrated channel.

[@EugeneKhutoryansky]

Thanks!

[@pendalink]

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

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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

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

[@EugeneKhutoryansky]

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

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Pure Love towards teaching. Thanks for the explanation.

[@EugeneKhutoryansky]

Thanks.

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Real quality and effort making these videos. Thank you!

[@EugeneKhutoryansky]

Thanks for the compliment about my videos.

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[@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.

[@Mau365PP]

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

[@EugeneKhutoryansky]

Glad you liked my video. Thanks.

[@FingerThatO]

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

[@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....

[@cript3232]

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

[@EugeneKhutoryansky]

Thanks for the compliment.

[@jimlbeaver]

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

[@EugeneKhutoryansky]

Thanks. I am glad you liked my video.

[@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.

[@shezeeblanka1611]

this is an absolute gem.

[@EugeneKhutoryansky]

Thanks. I am glad you liked my video.

[@mareialgarni2012]

Amazing explanation and visualization

[@EugeneKhutoryansky]

Thanks for the compliment.

[@11Petrichor]

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

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This is really impressive. Nice work

[@EugeneKhutoryansky]

Thanks for the compliment.

[@majdwahbi44]

Perfectly explained! Thanks

[@EugeneKhutoryansky]

Thanks. Glad you liked my explanation.

[@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..

[@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.

[@Hustleandstack]

this channel is groundbreaking

[@EugeneKhutoryansky]

Thanks.

[@alexjimenez6020]

Amazing graphic explanation!!

[@EugeneKhutoryansky]

Thanks.

[@realcygnus]

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

[@EugeneKhutoryansky]

Thanks for the compliment.

[@sandorszabo2470]

The music is also excellent.

[@EdneiBloemer]

absolutely LOVE your videos, keep it up!

[@DDDelgado]

Great explanation for linearity in a system

[@gepisar]

at 8:35 you say that the rate in change of the state can be represented by a vector. (White arrow) This vector is also changing? And can THAT change in vector be represented by another vector? Do these vectors have names? (Like the change in velocity is called acceleration and the change in acceleration is called a jerk?)

[@maksudjonusmonov5711]

Wow, so much meaning in one video.

[@EugeneKhutoryansky]

Thanks.

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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 ! :)

[@walfluca]

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

[@EugeneKhutoryansky]

Thanks. I am glad you liked my video.

[@jairoandresguevarajulio571]

It was a very useful explanation. Thank's.

[@EugeneKhutoryansky]

Glad you liked my explanation. Thanks.

[@ridiculous_]

the most wanted topic

[@fredericbastiat5502]

Superb as always!

[@EugeneKhutoryansky]

Thanks for the compliment.

[@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.

[@hasankaynak2253]

very clear explanation. thank you very much.

[@EugeneKhutoryansky]

Thanks. I am glad you liked my explanation.

[@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

[@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.

[@kipropkigz1285]

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

[@EugeneKhutoryansky]

Thanks.

[@AsifShah-fi7oj]

@Physics Videos by Eugene Khutoryansky How about taking gravity out of picture in the ball, hill & valley example? I guess equilbrium is a relative term.

[@prashannashrestha9791]

too much love for your video...thank you

[@EugeneKhutoryansky]

Glad you liked my video.

[@Jakenheimer1]

I love this channel

[@EugeneKhutoryansky]

I am glad to hear that. Thanks.

[@R3DPandaLP]

you make the complicated seem simple

[@EugeneKhutoryansky]

Thanks.

[@Xinvoker]

The Legend

[@MrLegolando]

Great explanation

[@EugeneKhutoryansky]

Thanks for the compliment. I am glad you liked it.

[@andrewdavis6191]

another amazing video!

[@EugeneKhutoryansky]

Thanks. I am glad you liked it.

[@drmichaelhz]

just perfect explanation :)

[@adhamosama7531]

amazing video congratulations

[@EugeneKhutoryansky]

Glad you liked it. Thanks.

[@nerdinvestdor]

This video was really cool thanks man!

[@EugeneKhutoryansky]

Glad you liked it. Thanks.

[@alphablondy04]

finally back!

[@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.

[@ben-2368]

Thank you. This is very helpful.

[@EugeneKhutoryansky]

You are welcome and thanks.

[@quantumsigmaqed6312]

Like your videos a lot. :D Keep going!

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Every curious person seek for contents like these for free.

[@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.

[@Barzi2001]

This was awesome. Do you also have a Lyapunov stability direct method video like this?

[@DrPepper776]

i fall asleep to these videos :)

[@bdedi]

best channel

[@EugeneKhutoryansky]

Thanks for the compliment.

[@manos1779]

Great video 😍😍😍

[@EugeneKhutoryansky]

Thanks. Glad you liked it.

[@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.