Zwiebach Problem 8.6: Explaining "We Do Not Use the Equations of Motion

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The discussion centers on Zwiebach's Problem 8.6, specifically the phrase "we do not use the equations of motion." A participant expresses confusion after applying the equations of motion and arriving at a different answer than Zwiebach's solution. The key takeaway is that the problem requires a conceptual understanding that transcends standard equations of motion, emphasizing the importance of the Lagrangian framework in this context.

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Homework Statement


Here is Zwiebach's solution to Problem 8.6.

Can someone explain the sentence "we do not use the equations of motion".

I used the equations of motion and I got a completely different answer!


Homework Equations





The Attempt at a Solution

 
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Sorry. I stupidly forgot to upload the attachment. Anyway above the parenthetical that says note that we do not use the equation of motion, I used the equation of motion to get

[tex]\delta L = \epsilon \frac{d}{dt}(\frac{\partial L}{\partial \dot{q}} \dot{q} )[/tex]

And the rest is totally different for me.

So, why can I not use the equation of motion here?
 

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