It is like I'm being taught by a floating head and hands. This is great!
@richard_pates
3 жыл бұрын
hahaha, yes indeed! I've finally found my true calling :)
@arnold-pdev
7 ай бұрын
the way you motivate the properties of the lyapunov function is so natural, and puts this lesson leaps and bounds beyond the others i've seen. now, the lesson will stick. thank you
@elijahgemmill2000
21 күн бұрын
You explained in 10 minutes what my university couldn't explain in 60.
@MeinHerrDreyer
11 ай бұрын
This is an amazingly intuitive explanation, especilaly the part about the dot product towards the end, thank you!
@gokhandemirkiran1134
3 жыл бұрын
Great. I have been searching for Lyapunov function properties. Especially to understand the intuitive idea about Vdot(x) = Grad(x)f(x)
@raoufmagdy3661
3 жыл бұрын
The best explaining video (and material) I have found on internet... Great Job and keep going
@StrrikerGr
2 жыл бұрын
It's so funny when your University teachers make theorems SOOOO damn difficult to understand and you find a 10 min video that explain a 2 hour Lecture+ better,simpler and much easier to understand. Perfect explanation,thx for saving lives here!!
@richard_pates
2 жыл бұрын
Thanks so much for the feedback, I really appreciate it. My experience is overwhelmingly that most things do have simple explanations. So keep doing what you're doing - if you find something confusing, go explore and study for yourself, there is likely a simple explanation out there!
@M30W3R
2 жыл бұрын
Thanks for the explanation, literature and websites had me worried but it's much simpler than what I thought.
@richard_pates
2 жыл бұрын
Glad it helped!
@hafezghaemi6237
2 жыл бұрын
Beautifully explained! Thanks!!
@bebarshossny5148
3 жыл бұрын
Made things super clear I can't thank you enough
@richard_pates
3 жыл бұрын
very happy to hear that. Good luck with your studies!
@amirhosseinafkhami2606
2 жыл бұрын
Very well, thanks for this great explanation!
@mukhtarsani9871
2 жыл бұрын
Great! An amazing explanations!!!
@victorli6999
2 ай бұрын
my man is the real hero
@kiamehrjavid7723
6 ай бұрын
Very very nice and well explained :thumbsup:
@imsparkly7968
2 жыл бұрын
fantastic explanation, thank you!
@ritikalohia7763
Жыл бұрын
sir, do you really write from right to left (in reverse)??
@richard_pates
Жыл бұрын
It would be an awesome party trick - but the truth is unfortunately more dull. I'm just mirroring in post production...
@pijushpanday3509
Жыл бұрын
Great explanation
@abuzerdogan3175
9 ай бұрын
perfect explanation
@eric3813
3 жыл бұрын
Wow, awesome video, thank you!
@cessromer7078
13 күн бұрын
How do you approach to a general solution for stability from a stand point of a LYAPUNOV functions for a class of nth order nonlinearar differential equations?
@AmanKumar-fr1ox
3 жыл бұрын
Awsome
@M-dv1yj
3 ай бұрын
Omg ur the Son of the Red Dwarf computer 👏🏽
@richard_pates
3 ай бұрын
hahaha - a blast from the past, but spot on!
@jemimitu1557
3 жыл бұрын
Thank you for sharing.
@richard_pates
3 жыл бұрын
My pleasure - hopefully it was useful!
@GeoffryGifari
Жыл бұрын
huh it almost seems like Lyapunov function applies generally to dynamical systems and "potential energy" is just the one used in classical mechanics
@richard_pates
Жыл бұрын
Brilliant question - and it sounds like you found the answer already. There are very strong senses in which a Lyapunov function is guaranteed to exist. For example, if I have a system \dot{x}=f(x) which is globally asymptotically stable, there will always be a Lyapunov function that proves it. So it is rather like a very precise generalisation of the concept of potential energy, but for general dynamic systems as you say - very cool stuff! A slight note of caution though - I'm a bit fuzzy on the precise details myself, but I believe you can also prove things like: finding a Lyapunov function is in general as difficult as solving the original differential equation for all initial conditions. And if you can do this, you wouldn't need the Lyapunov function anymore. And to make things worse, lots of the usual tricks you might think of to approximate them - for example approximating the set of all Lyapunov functions by some nice function classes (for example sum of squares polynomials) - also might not work. That is given a globally asymptotically stable dynamical system, the Lyapunov function that proves it might not be differentiable or smooth. So while it is very nice to know that a function exists, don't expect any free lunches!
@pnachtwey
24 күн бұрын
had that figured out before I had even heard of lyapunov. Isn't this obvious?
@GeoffryGifari
Жыл бұрын
for an arbitrary dynamical system, does Lyapunov function always exist?
@joschistep3442
Жыл бұрын
No. It can only exist around an asymptotically stable equilibrium. (We can prove that an equilibrium is asymptotically stable by showing that a Lijapunov function exists there.)
@brendawilliams8062
2 жыл бұрын
Thankyou
@princefriendship
Жыл бұрын
Thanks a lot. Voice needs to be more clear.
@user-dp5nx8wo5d
3 жыл бұрын
Hello, can you help me please, I am working on bifurcations and solving a system of 3 equations with 6 variables and solving them using a Local Method of Lyapunov - Schmidt, I need some help please
@muzammilnaeem4687
2 жыл бұрын
its definitely black magic hehehe
@zilowa8779
2 жыл бұрын
Akıl mantık işi değil, Barış hocaya selamlar.
@t.p.2305
Жыл бұрын
Audio quality could be better
@tıbhendese
3 ай бұрын
I am outsider of the topic, I have a homework, and I understand nothing about it
Пікірлер: 42