Euler-Lagrange equation application

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Homework Help Overview

The discussion revolves around the application of the Euler-Lagrange equation in a specific problem context. Participants are exploring how to manipulate the equation and relate it to a standard derivative, as well as addressing the differences between the two forms.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss attempts to manipulate the Euler-Lagrange equation and express confusion regarding the differences between it and the standard derivative. Questions arise about the application of derivative rules and the reasoning behind the results obtained.

Discussion Status

The discussion is ongoing, with some participants suggesting alternative approaches, such as calculating the standard derivative instead of using the Euler-Lagrange equation. There is a request for further clarification on the derivative rules being applied, indicating a productive exchange of ideas.

Contextual Notes

Participants are navigating the complexities of derivative rules and their application in the context of the Euler-Lagrange equation, with some uncertainty about the necessary steps to achieve the desired form of the equation.

Ascendant78
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Homework Statement



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Homework Equations



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The Attempt at a Solution



I have tried manipulating the equation a few different ways, but the Euler-Lagrange and the one I'm supposed to show for a) is so different that I just can't seem to work. Can someone please point me in the right direction here?
 
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I think you don't need the Euler-Lagrange equation for (a). That looks like the standard derivative, just calculate it.
 
Well, just calculating the derivative, I'm not sure why it is coming out the way it is? I get that the "t" component would be zeros, cancelling out its parts. However, I'm not sure what derivative/partial derivative rules are being applied to get the equation to look like the one asked for in a)?
 
Think chain rule. If you still can't figure it out, show us your attempt.
 

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