Using the Euler-Lagrange Equation to prove that the shortest path between two points on a plane is a straight line. Download notes for THIS video HERE: bit.ly/2OSYYtl Download notes for my other videos: bit.ly/37OH9lX
Пікірлер: 40
@spandansreyanshupadhee3 жыл бұрын
You actually deserve views in millions sir , the concept really helped me to understand the Fermat's principal
@davidbrisbane72063 жыл бұрын
Great video. You deserve to get a large subscriber base.
@JohnSmith-kj2od3 жыл бұрын
I kid you not, I got a handout(about 4 days ago) after learning Newtonian mechanics and out of the 6 problems, two of them use concepts that were recommended to me by this channel on the same day, I just have incredible luck
@ha15224 Жыл бұрын
Thank you for these videos sir, I am currently reviewing/brushing up on my studies to prepare for graduate school applications (aerospace engineering major) and you have been an immense help. This channel is on the levels of 3b1b and Eugene Khutoryansky and deserves millions of views.
@claudefazio3 жыл бұрын
Very well explained! I enjoy your calm style of presentation.
@ozgurartvin5 ай бұрын
tHANK YOU VERY MUCH. gREAT LECTURE
@faheemgulzar14 ай бұрын
Excellent videos
@manmis0073 жыл бұрын
Waiting for some time before I see you again with some grt stuff again.......
@jmsolangi7 ай бұрын
Thanks, very helpful and clear
@amukelaniebenezer4063 жыл бұрын
Very simply explained
@hadsonwafula37519 ай бұрын
Thank you it is very much useful
@andrerossa85533 жыл бұрын
Thanks for such a simple and clear explanation. By the way which application do you use to write on the screen?
@Freeball993 жыл бұрын
The app is called "Paper" by WeTransfer running on an iPad Pro 13 inch and using an Apple Pencil. Screen capture is recorded by attaching the iPad to my Mac and using Quicktime.
@andrerossa85533 жыл бұрын
Thank you very much for your prompt reply. You're the best!!
@Rafael-c9c3 жыл бұрын
Great video! You got +1 sub. Which hardware do you use to illustrate this video?
@Freeball993 жыл бұрын
The app is called "Paper" by WeTransfer running on an iPad Pro 13 inch and using an Apple Pencil. Screen capture is recorded by attaching the iPad to my Mac and using Quicktime.
@prerakvaishnav75123 жыл бұрын
Thank you this explains quite bit of minimization approach 😀
@claudiogomes2493 Жыл бұрын
Thank you so much
3 жыл бұрын
Sir, since I discover your channel some months ago, I've been following you! You're doing a huge, beautiful and awsome worke with this videos. I would like to ask for recommendations to practice this theory. Maybe if you know an excerse book or something like that. Thanks in advance!
@Freeball993 жыл бұрын
If you're talking about books the explain Variational methods, these are very good: 1. "Solid Mechanics A Variational Approach" By Clive L. Dym, Irving H. Shames 2. "Energy And Finite Element Methods In Structural Mechanics" By Irving Shames and Clive Dym
3 жыл бұрын
@@Freeball99 thanks for your quick answer. But more than theory, I'm looking for problems to apply what I have learned from you. I guess books will have good problems for that! Thanks!
@Freeball993 жыл бұрын
For the introductory stuff, "Mechanical Vibrations" by SS Rao is useful. It has some errors, but lots of problems for you to work.
@Pedritox0953 Жыл бұрын
Great video!
@workerpowernow2 жыл бұрын
very helpful. Thanks
@abcd-gp6is2 жыл бұрын
Thank you ❤️❤️❤️
@spencergee69482 жыл бұрын
Your verba presentation is first class. Do I detect a South African origin?
@Freeball992 жыл бұрын
Yup. Grew up in Durban!
@dogeness3 жыл бұрын
Thanks this was really helpful. I just have one small question. You didn’t use del(I)=0 (equation 3) in the solution, did you? So why did you write it down?
@Freeball993 жыл бұрын
The result of setting δI = 0 yields the Euler-Langrange Equation. By setting δI = 0, I was showing that we could use the results of the previous video (the E-L Equation) to give us the solution.
@shevek59348 ай бұрын
Am I understanding it correctly that this argument for the path being a straight line doesn't depend at all on the specific Lagrangian for the distance, but would be true for any functional that depends only on either y or y' but not both?
@Freeball998 ай бұрын
I'm not sure I understand the part of your question about the functional depending only on y. I think just about any path integral would have a y' component to it - perhaps you have an example.
@jaafars.mahdawi6911 Жыл бұрын
I can guarantee that your final hope (that this video was useful) has been granted. Only a minor detail seems in place, namely, in eq.7, the constant cannot be 1. Homework for fellow viewers: can you tell why, like, intuitively?
@haric_ Жыл бұрын
How do you proof that y' has to be a constant in the first place?
@ccdavis943032 жыл бұрын
Thanks.
@NoName-rn8uk3 жыл бұрын
Brilliant
@GreenMeansGOF9 ай бұрын
Not boring at all. I am curious however, if there is a more elementary proof. Say a Euclidean/Coordinate Geometry proof.
@Freeball999 ай бұрын
I'm not familiar with any other proofs, but I am sure they exist.
@cana5312 Жыл бұрын
Could you cover the shortest distance between the two points on the arbitrary plane, not the 2D plane?
@Freeball99 Жыл бұрын
Yes, I'll get there eventually. I have this on list a video to make on the shortest distance between two points on a sphere (a geodesic). However, I have a few others to make before that.