A Particle in a Potential Well: Nonlinear Dynamics

[@virgenalosveinte5915]

Steve this whole playlist is so insanely valuable. I'm not sure if you're aware of how much each viewer cherishes these videos. Highest quality educational content on youtube!! (tied with 3blue1brown)

[@ArtisanTony]

The most impressive thing is how he stands behind the glass and writes in reverse :)

[@alpaciandecatre4385]

No🤣. He is left handed. Writes normally and the video is flipped horizontally..

[@Anhtuan-qm6gi]

@@alpaciandecatre4385 there was a video in which he wrote in normal direction but after he realized that, he wrote in inverse. I don't really know but it seems that he actually writes in inverse

[@juanmanuelmillansanchez8165]

Your dedication is simply jaw dropping. I'm really enjoying your differential equation playlist. Thanks for all the awesome content!

[@jaim3m3s]

this is such incredible quality

[@kambizmerati1119]

Fascinating as always!

[@ireoluwaTH]

Can't wait for the next video! Thank you...

[@zjason7582]

R:11:31, my calculation outcome isV = mg(1-cosθ), so eventually θ''= (-g/L)sinθ, do you have any insight?

[@limewnek1542]

How we can modeling wind energy using pde

[@YusiiVerse]

okay..but how is potential energy related to V(x)?

[@seslocrit9365]

Why is it partial of x over total derivative even though its constrained to one dimension?

[@Nickname006]

Total derivative would also include time.

[@seslocrit9365]

@@Nickname006 wrt to what?

[@Nickname006]

@@seslocrit9365 It is just better notation to use partial derivatives here, because force is the gradient of potential energy. Gradient includes partial derivatives of position coordinates.

[@cafebrasileiro]

In this example it works both ways. But suppose V is time-dependent: V = V (x,t) . Then using partial and total derivatives would give you different results, even though it's one dimension.

[@seslocrit9365]

@@cafebrasileiro right, I just realized that. I'm an idiot

[@Srinivasa-no-eqn-without-god]

Thank sir for your incredible service, I have a dought that can I consider lid driven cavity as a portrait if so can I have homoclinic orbit , and what kind of point we can analyze.? Thanks sir 🙏

[@danieljulian4676]

You know what they say in court, Kumar: Never ask a question the answer to which you don't already know.

[@sekus]

Great work on getting Newton's equation using both methods. However, in the Euler-Lagrange method, I feel that there's a missing mass in your kinetic equation. I believe in the pendulum example the mass cancels out. Can you quickly go over this?

[@GeoffryGifari]

huh didn't he set the mass to 1 to simplify?

[@sudarshanpoudyal5089]

What is the physical interpretation of Euler Lagrange equation does it mean kinetic energy = potential energy

[@seslocrit9365]

It is a reformulation of newton's law by using "action." The advantage is that it uses generalized co-ordinate. For example, try deriving the equation of motion for a double pendulum. Now lookup doing it with the Euler-Lagrange equation. It's a lot easier with generalized coordinates. It's an essential bedrock of modern physics. This is about the limit of knowledge on the topic.

[@sudarshanpoudyal5089]

@@seslocrit9365is it f - ma = 0

[@seslocrit9365]

@@sudarshanpoudyal5089 , in this case, yes, but when dealing with other systems like Quantum Mechanics, not necessarily. Watch this video kzbin.info/www/bejne/q3fRhYWAZ8eYbas This is about the limit of my knowledge, to be honest.

[@lioneloddo]

I don't know why but I had always though to the Sysiphus myth. If only the mechanical energy had greater than the potential energy ... In quantum mechanics, the curse would have been defeated too...

[@fishbones92]

Pardon me, but I’d love me some clues of how to go about solving the solutions for a sphere potential well Awesome

[@ardiris2715]

I wonder how of that a high school grad who took HS physics and HS calculus would understand. 90%? (:

[@Jibs-HappyDesigns-990]

don't fall 4 apple! it can make it's own sauce! Isaac Newton. don't fall 4 apple! though it made lots of potential, it still fell 2 get off the ground? bummer! ;) not trying 2 bruise the humor, I'll try the funny bone! Oo(... all stars Prof Steve! those apples R gett'n ripe!