Understanding the Euler Lagrange Equation

To understand classical mechanics it is important to grasp the concept of minimum action. This is well described with the basics of calculus of variations. In this lecture I explain how to derive the Euler Lagrange equation, which we will use later to solve problems in mechanics related to minimum action.
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[@ryanj748]

This is the best, clearest, and most enthusiastic presentation of Euler-Lagrange equation I've seen. Thank you, sir.

[@DrJuanKlopper]

Thanks Ryan. I appreciate it.

[@willemvanoranje1533]

Strange that there aren't any comments yet. Thanks for your explanation.

[@DrJuanKlopper]

The comments were never turned on. My bad.

[@abufares1223]

Since 2014, this video still gives a comprehensive explanation of the Euler Lagrange Equation that helps many students like me. Good job..thank you so much.

[@DrJuanKlopper]

Thank you so much!

[@alwyndsouza2351]

I have seen many explanations of Euler-Lagrange equation. This is the best one yet! Thank you.

[@DrJuanKlopper]

Thank you so much Alwyn.

[@JohnSmith-kj2od]

I can't thank you enough, I don't have the time to gain comfort in multivariable calculus but always need to understand this equation, I honestly cannot convey how much of a blessing this lecture is

[@DrJuanKlopper]

Hi John. That is very kind of you. I am happy that the video could be of help.

[@kamiljan1131]

I love the fact that you see so much beauty in it! That's probably the best way math can be taught. Can't thank you enough!

[@relebohileinnocent1550]

What a vivid explanation! From now on I am your student. Compares to videos of Lagrangian equation derivation I have seen on TH-cam, you are the best.

[@DrJuanKlopper]

You're very welcome! Thank you for the kind words.

[@ganeshiyer6653]

This isn’t knowledge or intelligence, just sheer wisdom!

[@DrJuanKlopper]

Many, many thanks Ganesh.

[@ilikecucumbers4223]

thanks the video helped me a lot because im trying to understand this stuff without a background in multivariable calculus and you explaining the basics really helped

[@DrJuanKlopper]

Glad it helped! Cucumbers? Not my favorite, but I eat it :)

[@amitmaurya4566]

Thank you from India it really helped me , as i most professor skips this derivation.

[@DrJuanKlopper]

Glad it helped Amit!

[@henk_iii]

Dankie tog vir Dr. Klopper!!

[@DrJuanKlopper]

My plesier Henk.

[@jwarha7797]

This is beautiful maths indeed. Thank you.

[@nickpgr10]

Your explanation is the best one so far sir. Thanks many many times. Please upload videos on port hamiltonian systems if it is possible for you.

[@DrJuanKlopper]

Thank you very much for the kind words Nikhil.

[@rangamurali7667]

Prof doing an incredibly outstanding job of explaining the derivation, sorry for mistyping earlier.

[@ombie9439]

Thank you for the great explanation Sir!!..felt like Rowan Atkinson himself teaching us Math

[@DrJuanKlopper]

Now that put a smile on my face! Thanks.

[@johnmosugu]

Thank you very much Juan Klopper for this wonderful video on Euler-Lagrange equation! You made Calculus of variations look so easy. I think I prefer the part you used the chain rule for partial differentiation. I have not been able to understand the Taylor series expansion approach. Can you make a video on that too?

[@pantelisnikolaou6956]

Thank you so much sir for this video. Beautifully explained.

[@FranckRussia]

This is a great video saving my life 😃😃
Thank you sir

[@sandnerdaniel]

Great lecture on the principle of least action!

[@DrJuanKlopper]

Thanks Daniel.

[@lazemjam7747]

Thank you very much for this lecture

[@lucacolla]

Standing ovation

[@DrJuanKlopper]

Thank you very much Luca. This comment made my day.

[@YualChiek]

Excellent explanation!

[@danieldiaz-xi5bw]

Pretty awesome Video ! greetings from Mexico 🇲🇽!

[@DrJuanKlopper]

Hey, thanks Daniel. I visited Mexico a few years ago. Just rented a car and explored the country. It was a wonderful experience.

[@md.rumman5754]

Thanks a lot sir.

[@DrJuanKlopper]

Most welcome. My pleasure.

[@NoNTr1v1aL]

Amazing video!

[@DrJuanKlopper]

Thank you Mohammed.

[@charlesokoh3373]

incredible
nice video

[@DrJuanKlopper]

Thank you very much!

[@zweisteinya]

Change the 't' to an 'x' and you get "the Calculus of Variations"

[@snowpanther8092]

D