Derivation of the Euler-Lagrange Equation
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- Опубликовано: 15 окт 2022
- 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.
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!!!
I’m very glad the derivation was helpful! I also wish I’d had a fully explained derivation for the equation in advance. Hence, the reason for the video. All the best!
I was searching for this type of explanation for a while,congratulations,keep it up :)
I’m glad you found it useful!
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!
Glad you enjoyed the video! I hope to make another derivation video similar to this one in the near-future. See you there then, potentially!
Very very very interesting! Thanks you very much !!!
Glad you found it useful!
Taylor's Classical Mechanics is a great book :)
Very good!
Thank you!
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?
@@Arriyad1 hi there! You are most definitely right. Taylor’s Classical Mechanics seems to use y(x) with x as a placeholder technically for q (any canonical coordinates). But for the purpose of stating that this gives you a path optimalizing function, y(t) may indeed have been more intuitive. Thank you for the observation!