Lagrangian: How did they get from this step to the other?

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The discussion focuses on the derivation of terms in the Lagrangian mechanics equation, specifically addressing the confusion surrounding the third term in equation 5.192. Participants clarify that the term arises from differentiating the mℓ̇θcos(θ) component, which includes two instances of θ, leading to two distinct terms. The conversation emphasizes the importance of understanding how each term contributes to the overall equation, particularly in relation to the variables involved.

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Homework Statement


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The Attempt at a Solution


I don't understand where the third term from the first equation of 5.192 come about.. as clearly L doesn't depend on x at all, so ∂L/∂x should be zero.

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The second and third terms both come from differentiating the m\ell\dot{\theta}\cos{\theta} term...you get two terms because there are two \theta's in it.
 
Last edited:
Chopin said:
The second and third terms both come from differentiating the m\ell\dot{\theta}\cos{\theta} term...you get two terms because there are two \theta's in it.

ah that makes sense! thanks a lot!
 

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