Undergrad Lagrangian and the Euler Lagrange equation

[Hamiltonian]

TL;DR

I don't understand why the Euler Lagrange equation holds true.

I am new to Lagrangian mechanics and I am unable to comprehend why the Euler Lagrange equation works, and also what really is the significance of the lagrangian.

 

[anuttarasammyak]

Have you read Feynman's lecture of
https://www.feynmanlectures.caltech.edu/II_19.html ?
It might help you.

 

[saulbush]

Have you read Feynman's lecture of
https://www.feynmanlectures.caltech.edu/II_19.html happy wheels ?
It might help you.

One of my favorite memories from classical mechanics!