How do you get this result (mechanics)? quick question (1 Viewer)

sadpwner · Jun 22, 2015

lol

InteGrand · Jun 22, 2015

sadpwner said:
lol

It's basically the chain rule.

$$\frac{\mathrm{d}}{\mathrm{d}\theta}\left(\frac{1}{2}\dot{\theta}^2 \right)=\frac{\mathrm{d}}{\mathrm{d}\dot{\theta}} \left( \frac{1}{2} \dot{\theta}^2 \right)\times \frac{\mathrm{d}\dot{\theta}}{\mathrm{d}\theta}= \dot{\theta}\frac{\mathrm{d}\dot{\theta}}{\mathrm{d}\theta}$.$

$(You may be more familiar with it in this form: $\ddot{x}=v\frac{ \mathrm{d}v}{\mathrm{d}x}=\frac{ \mathrm{d}}{ \mathrm{d}x}\left(\frac{1}{2}v^2 \right)$. It's the same idea.)$

How do you get this result (mechanics)? quick question (1 Viewer)

sadpwner

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InteGrand

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