Derivation of the Euler-Lagrange Equation

One of the most useful equations in classical mechanics is the Euler-Lagrange equation. Which allows one to use the principle of least action to solve various otherwise challenging problems. In this video, I derive the Euler-Lagrange equation using the least amount of pre assumed assumptions.

[peterasamoah]

This is by far the best video I've ever watched on this subject and I've seen tons of them. You explained everything so clearly showing each step with enough detail so that I'd fully understand and appreciate the proof for this derivation. Thank You so much!!!

[kenankenan]

Crystal and intuitive explanation. Thank you for sharing such a good high level videos on topic

[Cardaverr]

Best derivation in internet. Can't be clearer than this. Thank you.

[nicknametsouk]

amazing gem of a video, thank you so much! I also loved the music, was jamming out at the same time as discovering the secrets of nature, thank you!

[stephencolumbus]

I was searching for this type of explanation for a while, congratulations, keep it up :)

[rbam]

Very very very interesting! Thanks you very much !!!

[reefu]

Taylor's Classical Mechanics is a great book :)

[Arriyad]

If one writes y=y(x), then not all curves drawn are admissible, as some do not represent functions. I would rather have written y(t) and x(t) so as to represent all possible functions, with t something like time. What do you think?