Finding the path of least action (part 3)

Рет қаралды 22,199

PhysicsHelps

11 жыл бұрын

The conclusion of the derivation. F=MA! ... still

Пікірлер: 22

@AtmosphericRay 9 жыл бұрын

First time I've really ever understood lagrangian, thank you so much.

@raylittlerock3940 3 жыл бұрын

It clearly shows the analogy between the shortest distance between 2 points problem and the least action problem. Thanks for this!

@PhysicsHelps 10 жыл бұрын

I messed up writing it. I wrote a "d" instead of a "d/dt". Thanks for catching, and I made a note about it. Hopefully it's clear now. If not, I'm happy to clarify.

@TheDavidlloydjones 6 жыл бұрын

Hey, fella, we don't care about how you wrote it on your first time. We care about the fact that you published it after you found your mistake. When you find you've fucked something up totally, what you do is you erase it and you re-record it. To do otherwise is to give us all a great big finger: you hold us in contempt: it's not worth your while to care. You don't care about making an idjit of yourself in public. "Product rule. I may have said chain rule earlier. I don't know..." That's insane: it's on tape. You can go back and find out, then fix it! According to the info above you have now performed your fuck-up 14,000 times, wasting 14,000 people's time! Way to go: you're a pro! A professional, big-time, public time-waster. Fool!

@PhysicsHelps 10 жыл бұрын

The video is just named "Euler-Lagrange equation". It's meant not to require this three part series, so I just gave it its own name. You're right that there could be more organization. The videos are in playlists, but it seems like most people don't use them that way. I thought about making a website, but time is an issue.

@byrongibby 5 жыл бұрын

So to check my intuition, we reasoned 1) That there is some path that must minimise the action 2) For a path that minimises the action, small changes in the path should lead to only small changes in the action (consistent with the notion of a critical point) 3) The only path that is consistent with 2) is the path consistent with F = ma 4) Therefore the path of least action must be the one derived from Newton's second law Thank you so much for these lectures! I was stumbling in the dark before I saw your explanation of this and the related concepts.

@j.k.sharma3669 3 жыл бұрын

You explained concept of eta very well. Thanx

@burayhalalji9648 6 жыл бұрын

Brilliant videos!

@markovkin6046 9 жыл бұрын

Thanks for the great introduction to Lagrange! I'm taking a class on it the coming semester, and I was looking for an intro just like this. One thing, though: I like writing the eta with the right leg going down much further.

@zengrz 10 жыл бұрын

Wow, the last 3 videos were amazing! Thanks!

@simonjeffery5055 11 жыл бұрын

Really good. I'm not sure why more undergrads are not viewing your videos. Well done Physics help

@itan87ers 6 жыл бұрын

This helps me a lot!

@PhysicsHelps 10 жыл бұрын

The next video introduces the Euler-Lagrange equation as the result of a more generalized version of this process. I did this in rectangular coordinates because I think it's easier to understand that way. The general derivation of Euler-Lagrange is exactly the same as this, but with an "L" being carried around instead of the relevant pieces of the energy.

@PhysicsHelps 10 жыл бұрын

Thanks!

@Deuterium2H 10 жыл бұрын

Okay, fair enough. It just that I didn't see a "Part 4" video. So, I presume you must have named the next video in this series with a completely different title. KZfaq doesn't seem to provide a very intuitive order/sorting for how a series of videos is intended to be viewed...unless the original presenter maintains the exact same title, and only changes the suffix (e.g., part 1 of 4, part 2 of 4, etc.). Thanks for the clarification.

@jimdogma1537 11 жыл бұрын

I have absolutely no idea what you were doing with that equation starting at time 2:20. I've never seen a product rule used like that. It was unrecognizable. And I rewatched it 3 times. Too bad, because I was following the argument up until then.

@daemon7777 6 жыл бұрын

I know this answer comes very late but it migh help someone else with the same problem. He uses the product rule in the other direction. At the start we have something like: u*v' + u'*v and he uses the rule to get to (u*v)' Its not too complicated but I myself haven't seen he rule being applied in that direcion and also the notation is giving me a headache :)

@carloscruzarce9424 6 жыл бұрын

So.....how does F=ma tell us how to find the path of least action?

@Deuterium2H 10 жыл бұрын

What the heck...you didn't derive the Euler-Lagrange Equation...which is something you stated would be the purpose of these videos. Yes, you showed how Newton's second law is a result of applying principle of stationary action to the Lagrangian, but you did not provide a general proof / derivation of the E-L equation.

@orchoose 7 жыл бұрын

Actualy he did. He proved that E-L eq. is solution for path with least action hence we can use E-L eq. for calculating eq. of motion and be sure we are taking the right path :)

@matrixate 5 жыл бұрын

So, basically, this is a copy of the Feynman Vol 2 lecture on least action: www.feynmanlectures.caltech.edu/II_19.html Still...I liked it. Thanks bro.