What are the applications of Euler-Lagrange equations?

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The discussion revolves around the applications of the Euler-Lagrange equations within the context of classical mechanics. Participants are exploring foundational concepts related to the action integral and its stationary properties.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • The original poster expresses uncertainty about the topic and seeks guidance on how to approach the question. Some participants suggest focusing on key concepts related to the action integral and its relationship with the Euler-Lagrange equations. Others mention the differential equation associated with the Euler-Lagrange formulation and its significance in identifying stationary points.

Discussion Status

The discussion is ongoing, with participants providing insights into the theoretical aspects of the Euler-Lagrange equations. There is an acknowledgment of the basic nature of the question, and some guidance has been offered regarding the relationship between the equations and the action functional.

Contextual Notes

The original poster notes a lack of prior exposure to the topic and missing information in their notes, which may affect their understanding and ability to engage with the material fully.

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Below is the question:

[PLAIN]http://img706.imageshack.us/img706/7549/42541832.jpg

I don't even know where to start. there's nothing about this topic in my notes & I can't remember doing it before. I've tried searching for the key words but that didn't help much.

Does anyone have any links or suggestions as to how to start the question?

Thanks
 
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The keywords in the brackets are a good point to start - it is fundamental to classical mechanics that the Euler-Lagrange equations are equivalent to the action integral having a stationary value.
 
radou said:
The keywords in the brackets are a good point to start - it is fundamental to classical mechanics that the Euler-Lagrange equations are equivalent to the action integral having a stationary value.

Hmm I've done more reading, the differential equation I want is

dL/dx - d/dt[dL/dxdot] = 0

I believe? That gives the functional a stationary value... (ie stationary point, I'm guessing that's what extremal means)

Just seems a little silly that all I have to do is state a DE...
 
Yes, it seems like a basic theoretical question.

The equation you wrote down is the Euler Lagrange equation. Its solution are the functions for which the action functional is stationary.
 

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