Where can I find a comprehensive derivation of the Euler-Lagrange equation?

[ehrenfest]

Can someone link me to a thorough online derivation of the Euler-Lagrange equation from the principle of least action?

 

[smallphi]

http://en.wikipedia.org/wiki/Euler-Lagrange_equation

 

[denian]

The Euler-Lagrange equation is a fundamental equation in the field of mechanics, and it is derived from the principle of least action. This principle states that the path taken by a physical system between two points is the one that minimizes the action, which is a measure of the system's energy. The Euler-Lagrange equation is used to find the path that satisfies this principle.

There are many resources available online that provide a thorough derivation of the Euler-Lagrange equation. One such resource is the "Derivation of Euler-Lagrange equation" page on the Wolfram MathWorld website. This page provides a step-by-step derivation of the equation, including the necessary mathematical background and explanations of each step.

Another helpful resource is the "Euler-Lagrange Equation" lecture notes from the University of Cambridge's Department of Applied Mathematics and Theoretical Physics. These notes provide a detailed explanation of the derivation, along with examples and exercises for further practice.

Additionally, there are many online video tutorials and lectures available that walk through the derivation of the Euler-Lagrange equation. These can be found on platforms such as YouTube and Coursera.

it is important to always consult multiple sources and critically evaluate the information presented. I recommend exploring these resources and others to gain a thorough understanding of the derivation of the Euler-Lagrange equation.